Artículos de revistas: "Navier-Stokes, Equations de"

1

Rannacher, Rolf. "Numerical analysis of the Navier-Stokes equations". Applications of Mathematics 38, n.º 4 (1993): 361–80. http://dx.doi.org/10.21136/am.1993.104560.

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2

Acevedo Tapia, P., C. Amrouche, C. Conca y A. Ghosh. "Stokes and Navier-Stokes equations with Navier boundary conditions". Journal of Differential Equations 285 (junio de 2021): 258–320. http://dx.doi.org/10.1016/j.jde.2021.02.045.

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3

Acevedo, Paul, Chérif Amrouche, Carlos Conca y Amrita Ghosh. "Stokes and Navier–Stokes equations with Navier boundary condition". Comptes Rendus Mathematique 357, n.º 2 (febrero de 2019): 115–19. http://dx.doi.org/10.1016/j.crma.2018.12.002.

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4

Cholewa, Jan W. y Tomasz Dlotko. "Fractional Navier-Stokes equations". Discrete and Continuous Dynamical Systems - Series B 22, n.º 5 (abril de 2017): 29. http://dx.doi.org/10.3934/dcdsb.2017149.

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5

Ramm, Alexander G. "Navier-Stokes equations paradox". Reports on Mathematical Physics 88, n.º 1 (agosto de 2021): 41–45. http://dx.doi.org/10.1016/s0034-4877(21)00054-9.

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6

Reddy, M. H. Lakshminarayana, S. Kokou Dadzie, Raffaella Ocone, Matthew K. Borg y Jason M. Reese. "Recasting Navier–Stokes equations". Journal of Physics Communications 3, n.º 10 (17 de octubre de 2019): 105009. http://dx.doi.org/10.1088/2399-6528/ab4b86.

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7

Bensoussan, A. "Stochastic Navier-Stokes Equations". Acta Applicandae Mathematicae 38, n.º 3 (marzo de 1995): 267–304. http://dx.doi.org/10.1007/bf00996149.

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8

Capiński, Marek y Nigel Cutland. "Stochastic Navier-Stokes equations". Acta Applicandae Mathematicae 25, n.º 1 (octubre de 1991): 59–85. http://dx.doi.org/10.1007/bf00047665.

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9

Yang, JianWei y Shu Wang. "Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations". Science China Mathematics 57, n.º 10 (28 de febrero de 2014): 2153–62. http://dx.doi.org/10.1007/s11425-014-4792-4.

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10

Martin ‎, Andreas. "Mathematical-Physical Approach to Prove that the Navier-‎Stokes Equations Provide a Correct Description of Fluid ‎Dynamics". Hyperscience International Journals 2, n.º 3 (septiembre de 2022): 97–102. http://dx.doi.org/10.55672/hij2022pp97-102.

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This publication takes a mathematical approach to a general solution to the Navier-Stokes equations. The basic idea is a ‎mathematical analysis of the unipolar induction according to Faraday with the help of the vector analysis. The vector analysis ‎enables the unipolar induction and the Navier-Stokes equations to be related physically and mathematically since both ‎formulations are mathematically equivalent. Since the unipolar induction has proven itself in practice, it can be used as a ‎reference for describing the Navier-Stokes equations‎.

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11

Akysh, A. Sh. "The Cauchy problem for the Navier-Stokes equations". BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, n.º 2 (30 de junio de 2020): 15–23. http://dx.doi.org/10.31489/2020m2/15-23.

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12

Wu, Jiahong y Kazuo Yamazaki. "Convex integration solution of two-dimensional hyperbolic Navier–Stokes equations^*". Nonlinearity 37, n.º 11 (8 de octubre de 2024): 115014. http://dx.doi.org/10.1088/1361-6544/ad7f18.

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Abstract Hyperbolic Navier–Stokes equations replace the heat operator within the Navier–Stokes equations with a damped wave operator. Due to this second-order temporal derivative term, there exist no known bounded quantities for its solution; consequently, various standard results for the Navier–Stokes equations such as the global existence of a weak solution, that is typically constructed via Galerkin approximation, are absent in the literature. In this manuscript, we employ the technique of convex integration on the two-dimensional hyperbolic Navier–Stokes equations to construct a weak solution with prescribed energy and thereby prove its non-uniqueness. The main difficulty is the second-order temporal derivative term, which is too singular to be estimated as a linear error. One of our novel ideas is to use the time integral of the temporal corrector perturbation of the Navier–Stokes equations as the temporal corrector perturbation for the hyperbolic Navier–Stokes equations.

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13

Ju, Qiangchang y Jianjun Xu. "Zero-Mach limit of the compressible Navier–Stokes–Korteweg equations". Journal of Mathematical Physics 63, n.º 11 (1 de noviembre de 2022): 111503. http://dx.doi.org/10.1063/5.0124119.

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We consider the Cauchy problem for the compressible Navier–Stokes–Korteweg system in three dimensions. Under the assumption of the global existence of strong solutions to incompressible Navier–Stokes equations, we demonstrate that the compressible Navier–Stokes–Korteweg system admits a global unique strong solution without smallness restrictions on initial data when the Mach number is sufficiently small. Furthermore, we derive the uniform convergence of strong solutions for compressible Navier–Stokes–Korteweg equations toward those for incompressible Navier–Stokes equations as long as the solution of the limiting system exists.

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14

Bela Cruzeiro, Ana. "Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers". Journal of Geometric Mechanics 11, n.º 4 (2019): 553–60. http://dx.doi.org/10.3934/jgm.2019027.

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15

XU, KUN y ZHAOLI GUO. "GENERALIZED GAS DYNAMIC EQUATIONS WITH MULTIPLE TRANSLATIONAL TEMPERATURES". Modern Physics Letters B 23, n.º 03 (30 de enero de 2009): 237–40. http://dx.doi.org/10.1142/s0217984909018096.

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Based on a multiple stage BGK-type collision model and the Chapman–Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The new gas dynamic equations have the same structure as the Navier–Stokes equations, but the stress strain relationship in the Navier–Stokes equations is replaced by an algebraic equation with temperature differences. In the continuum flow regime, the new gas dynamic equations automatically recover the standard Navier–Stokes equations. The current gas dynamic equations are natural extension of the Navier–Stokes equations to the near continuum flow regime and can be used for near continuum flow study.

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16

Amrouche, Chérif y Ahmed Rejaiba. "Navier-Stokes equations with Navier boundary condition". Mathematical Methods in the Applied Sciences 39, n.º 17 (16 de febrero de 2015): 5091–112. http://dx.doi.org/10.1002/mma.3338.

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17

Youssef, Hairch, Abderrahmane Elmelouky, Mohamed Louzazni, Fouad Belhora y Mohamed Monkade. "A numerical study of interface dynamics in fluid materials". Matériaux & Techniques 112, n.º 4 (2024): 401. http://dx.doi.org/10.1051/mattech/2024018.

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This paper deals with the approximation of the dynamics of two fluids having non-matching densities and viscosities. The modeling involves the coupling of the Allen-Cahn equation with the time-dependent Navier-Stokes equations. The Allen-Cahn equation describes the evolution of a scalar order parameter that assumes two distinct values in different spatial regions. Conversely, the Navier-Stokes equations govern the movement of a fluid subjected to various forces like pressure, gravity, and viscosity. When the Allen-Cahn equation is coupled with the Navier-Stokes equations, it is typically done through a surface tension term. The surface tension term accounts for the energy required to create an interface between the two phases, and it is proportional to the curvature of the interface. The Navier-Stokes equations are modified to include this term, which leads to the formation of a dynamic interface between the two phases. The resulting system of equations is known as the two-phase Navier-Stokes/Allen-Cahn equations. In this paper, the authors propose a mathematical model that combines the Allen-Cahn model and the Navier-Stokes equations to simulate multiple fluid flows. The Allen-Cahn model is utilized to represent the diffuse interface between different fluids, while the Navier-Stokes equations are employed to describe the fluid dynamics. The Allen-Cahn-Navier-Stokes model has been employed to simulate the generation of bubbles in a liquid subjected to an acoustic field. The model successfully predicted the size of the bubbles and the frequency at which they formed. The numerical outcomes were validated against experimental data, and a favorable agreement was observed.

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18

He, Yinnian. "Finite Element Iterative Methods for the 3D Steady Navier--Stokes Equations". Entropy 23, n.º 12 (9 de diciembre de 2021): 1659. http://dx.doi.org/10.3390/e23121659.

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In this work, a finite element (FE) method is discussed for the 3D steady Navier–Stokes equations by using the finite element pair Xh×Mh. The method consists of transmitting the finite element solution (uh,ph) of the 3D steady Navier–Stokes equations into the finite element solution pairs (uhn,phn) based on the finite element space pair Xh×Mh of the 3D steady linearized Navier–Stokes equations by using the Stokes, Newton and Oseen iterative methods, where the finite element space pair Xh×Mh satisfies the discrete inf-sup condition in a 3D domain Ω. Here, we present the weak formulations of the FE method for solving the 3D steady Stokes, Newton and Oseen iterative equations, provide the existence and uniqueness of the FE solution (uhn,phn) of the 3D steady Stokes, Newton and Oseen iterative equations, and deduce the convergence with respect to (σ,h) of the FE solution (uhn,phn) to the exact solution (u,p) of the 3D steady Navier–Stokes equations in the H1−L2 norm. Finally, we also give the convergence order with respect to (σ,h) of the FE velocity uhn to the exact velocity u of the 3D steady Navier–Stokes equations in the L2 norm.

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19

Vyskrebtsov, V. G. "Integration of Navier-Stokes equations". Izvestiya MGTU MAMI 8, n.º 2-4 (20 de julio de 2014): 23–31. http://dx.doi.org/10.17816/2074-0530-67399.

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The author considers the integration of the motion equations of a Newtonian fluid (Navier-Stokes equations) in vector form, taking into consideration a separation of vector Navier-Stokes equation on the two equations containing separately linear and quadratic terms. On this basis, the paper demonstrates the possibility of integration of separated motion equations of an incompressible viscous fluid, which is determined in a greater extent by the characteristics of flow: boundary conditions, axisymmetric, nonaxisymmetric flow and others.

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20

Lefter, Adriana-Ioana. "Navier-Stokes Equations with Potentials". Abstract and Applied Analysis 2007 (2007): 1–30. http://dx.doi.org/10.1155/2007/79406.

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We study Navier-Stokes equations perturbed with a maximal monotone operator, in a bounded domain, in 2D and 3D. Using the theory of nonlinear semigroups, we prove existence results for strong and weak solutions. Examples are also provided.

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21

Constantin, P. "Euler and Navier-Stokes equations". Publicacions Matemàtiques 52 (1 de julio de 2008): 235–65. http://dx.doi.org/10.5565/publmat_52208_01.

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22

Breit, Dominic y Eduard Feireisl. "Stochastic Navier-Stokes-Fourier equations". Indiana University Mathematics Journal 69, n.º 3 (2020): 911–75. http://dx.doi.org/10.1512/iumj.2020.69.7895.

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23

Caraballo, Tomás y José Real. "Navier-Stokes equations with delays". Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 457, n.º 2014 (8 de octubre de 2001): 2441–53. http://dx.doi.org/10.1098/rspa.2001.0807.

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24

Mahalov, Alex. "Navier–Stokes Equations and Turbulence". European Journal of Mechanics - B/Fluids 22, n.º 5 (septiembre de 2003): 525–26. http://dx.doi.org/10.1016/s0997-7546(03)00061-x.

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25

Ling, Hsiao y Li Hailiang. "Compressible navier-stokes-poisson equations". Acta Mathematica Scientia 30, n.º 6 (noviembre de 2010): 1937–48. http://dx.doi.org/10.1016/s0252-9602(10)60184-1.

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26

Brzeźniak, Zdzisław, Gaurav Dhariwal y Mauro Mariani. "2D constrained Navier–Stokes equations". Journal of Differential Equations 264, n.º 4 (febrero de 2018): 2833–64. http://dx.doi.org/10.1016/j.jde.2017.11.005.

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27

Hu, Yuxi y Reinhard Racke. "Hyperbolic compressible Navier-Stokes equations". Journal of Differential Equations 269, n.º 4 (agosto de 2020): 3196–220. http://dx.doi.org/10.1016/j.jde.2020.02.025.

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28

Kuchugov, Pavel Alexandrovich y Vladimir Fedorovich Tishkin. "Partially averaged Navier-Stokes equations". Keldysh Institute Preprints, n.º 45 (2023): 1–19. http://dx.doi.org/10.20948/prepr-2023-45.

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Flows containing a transition to turbulence are inherent in a wide range of phenomena and processes, such as supernova explosions, combustion of gas mixtures, flow around bodies of various shapes, etc. Numerical simulation of such flows is of significant practical interest and is a complex independent task. To solve this problem, there are several main approaches in computational fluid dynamics, which have their own area of applicability, advantages and disadvantages. Thus, direct numerical simulation (DNS) and the large eddy simulation method (LES/ILES) are optimal approaches for describing flows in which there is a transition to turbulence, since they resolve a wide range of flow scales, but at the same time require significant computational resources due to the use of fine grids. Approaches based on the Reynolds Averaged Navier-Stokes equations (RANS) use a completely stochastic description of turbulence and have a significantly lower computational cost. At the same time, they allow one to describe only steady or slowly changing flows. A possible alternative is hybrid methods that combine the strengths of DNS/LES and RANS. In this paper, it is considered a hybrid approach based on partially averaged Navier-Stokes equations (PANS), which provides a seamless transition from RANS to DNS/LES. A detailed derivation of the corresponding system of equations and theoretical estimates characterizing the possibilities of the approach are given.

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29

Ju, Qiangchang y Zhao Wang. "Convergence of the relaxed compressible Navier–Stokes equations to the incompressible Navier–Stokes equations". Applied Mathematics Letters 141 (julio de 2023): 108625. http://dx.doi.org/10.1016/j.aml.2023.108625.

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30

Bresch, D., F. Guillén‐González, N. Masmoudi y M. A. Rodríguez‐Bellido. "Asymptotic derivation of a Navier condition for the primitive equations". Asymptotic Analysis 33, n.º 3-4 (enero de 2003): 237–59. https://doi.org/10.3233/asy-2003-546.

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This paper is devoted to the establishment of a friction boundary condition associated with the hydrostatic Navier–Stokes equations (also called the primitive equations). Usually the Navier boundary condition is used, as a wall law, for a fluid governed by the Navier–Stokes equations when we want to modelize roughness. We consider here an anisotropic Navier boundary condition corresponding to the anisotropic Navier–Stokes equations. By an asymptotic analysis with respect to the aspect ratio of the domain, we obtain a friction boundary condition for the limit system, that is the primitive equations. This asymptotic boundary condition only concerns the trace of the horizontal components of the velocity field and the trace of its vertical derivative.

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31

Dou, Changsheng y Zishu Zhao. "Analytical Solution to 1D Compressible Navier-Stokes Equations". Journal of Function Spaces 2021 (27 de mayo de 2021): 1–6. http://dx.doi.org/10.1155/2021/6339203.

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There exist complex behavior of the solution to the 1D compressible Navier-Stokes equations in half space. We find an interesting phenomenon on the solution to 1D compressible isentropic Navier-Stokes equations with constant viscosity coefficient on x , t ∈ 0 , + ∞ × R + , that is, the solutions to the initial boundary value problem to 1D compressible Navier-Stokes equations in half space can be transformed to the solution to the Riccati differential equation under some suitable conditions.

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32

Duan, Zhiwen, Shuxia Han y Peipei Sun. "On Unique Continuation for Navier-Stokes Equations". Abstract and Applied Analysis 2015 (2015): 1–16. http://dx.doi.org/10.1155/2015/597946.

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We study the unique continuation properties of solutions of the Navier-Stokes equations. We take advantage of rotation transformation of the Navier-Stokes equations to prove the “logarithmic convexity” of certain quantities, which measure the suitable Gaussian decay at infinity to obtain the Gaussian decay weighted estimates, as well as Carleman inequality. As a consequence we obtain sufficient conditions on the behavior of the solution at two different timest0=0andt1=1which guarantee the “global” unique continuation of solutions for the Navier-Stokes equations.

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33

Iftimie, Dragoş. "The 3D navier-stokes equations seen as a perturbation of the 2D navier-stokes equations". Bulletin de la Société mathématique de France 127, n.º 4 (1999): 473–517. http://dx.doi.org/10.24033/bsmf.2358.

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34

Henshaw, Willam D., Heinz-Otto Kreiss y Luis G. Reyna. "Estimates of the local minimum scale for the incompressible navier-stokes equations navier-stokes equations". Numerical Functional Analysis and Optimization 16, n.º 3-4 (enero de 1995): 315–44. http://dx.doi.org/10.1080/01630569508816621.

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35

Amrouche, Chérif y Ahmed Rejaiba. "Lp-theory for Stokes and Navier–Stokes equations with Navier boundary condition". Journal of Differential Equations 256, n.º 4 (febrero de 2014): 1515–47. http://dx.doi.org/10.1016/j.jde.2013.11.005.

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36

Li, Wei y Pengzhan Huang. "On a two-order temporal scheme for Navier-Stokes/Navier-Stokes equations". Applied Numerical Mathematics 194 (diciembre de 2023): 1–17. http://dx.doi.org/10.1016/j.apnum.2023.08.004.

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37

Dlotko, Tomasz. "Navier–Stokes–Cahn–Hilliard system of equations". Journal of Mathematical Physics 63, n.º 11 (1 de noviembre de 2022): 111511. http://dx.doi.org/10.1063/5.0097137.

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A growing interest in considering the “hybrid systems” of equations describing more complicated physical phenomena was observed throughout the last 10 years. We mean here, in particular, the so-called Navier–Stokes–Cahn–Hilliard equation, the Navier–Stokes–Poison equations, or the Cahn–Hilliard–Hele–Shaw equation. There are specific difficulties connected with considering such systems. Using the semigroup approach, we discuss here the existence-uniqueness of solutions to the Navier–Stokes–Cahn–Hilliard system, explaining, in particular, the limitation of maximal regularity of the local solutions imposed by the chosen boundary conditions.

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38

Zhang, Jie, Gaoli Huang y Fan Wu. "Energy equality in the isentropic compressible Navier-Stokes-Maxwell equations". Electronic Research Archive 31, n.º 10 (2023): 6412–24. http://dx.doi.org/10.3934/era.2023324.

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<abstract><p>This paper concerns energy conservation for weak solutions of compressible Navier-Stokes-Maxwell equations. For the energy equality to hold, we provide sufficient conditions on the regularity of weak solutions, even for solutions that may include exist near-vacuum or on a boundary. Our energy conservation result generalizes/extends previous works on compressible Navier-Stokes equations and an incompressible Navier-Stokes-Maxwell system.</p></abstract>

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39

Rozumniuk, V. I. "About general solutions of Euler’s and Navier-Stokes equations". Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, n.º 1 (2019): 190–93. http://dx.doi.org/10.17721/1812-5409.2019/1.44.

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Constructing a general solution to the Navier-Stokes equation is a fundamental problem of current fluid mechanics and mathematics due to nonlinearity occurring when moving to Euler’s variables. A new transition procedure is proposed without appearing nonlinear terms in the equation, which makes it possible constructing a general solution to the Navier-Stokes equation as a combination of general solutions to Laplace’s and diffusion equations. Existence, uniqueness, and smoothness of the solutions to Euler's and Navier-Stokes equations are found out with investigating solutions to the Laplace and diffusion equations well-studied.

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40

Kloeden, P. E. y J. Valero. "The weak connectedness of the attainability set of weak solutions of the three-dimensional Navier–Stokes equations". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, n.º 2082 (20 de marzo de 2007): 1491–508. http://dx.doi.org/10.1098/rspa.2007.1831.

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The attainability set of the weak solutions of the three-dimensional Navier–Stokes equations which satisfy an energy inequality is shown to be a weakly compact and weakly connected subset of the space H , i.e. the Kneser property holds in the weak topology for such weak solutions. The proof of weak connectedness uses the strong connectedness of the attainability set of the weak solutions of the globally modified Navier–Stokes equations, which is first proved. The weak connectedness of the weak global attractor of the three-dimensional Navier–Stokes equations is also established.

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41

Kim, Sun-Chul y Hisashi Okamoto. "Uniqueness of the exact solutions of the Navier—Stokes equations having null nonlinearity". Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, n.º 6 (diciembre de 2006): 1303–15. http://dx.doi.org/10.1017/s0308210500004996.

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We consider an overdetermined system of elliptic partial differential equations arising in the Navier–Stokes equations. This analysis enables us to prove that the well-known classical solutions such as Couette flows and others are the only solutions that satisfy both the stationary Navier–Stokes and Euler equations.

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42

Hamouda, Makram y Roger Temam. "Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary". gmj 15, n.º 3 (septiembre de 2008): 517–30. http://dx.doi.org/10.1515/gmj.2008.517.

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Abstract We prove the existence of a strong corrector for the linearized incompressible Navier–Stokes solution on a domain with characteristic boundary. This case is different from the noncharacteristic case considered in [Hamouda and Temam, Some singular perturbation problems related to the Navier–Stokes equations: Springer Verlag, 2006] and somehow physically more relevant. More precisely, we show that the linearized Navier–Stokes solutions behave like the Euler solutions except in a thin region, close to the boundary, where a certain heat equation solution is added (the corrector). Here, the Navier–Stokes equations are considered in an infinite channel of but our results still hold for more general bounded domains.

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43

Cruzeiro, Ana Bela. "Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review". Water 12, n.º 3 (19 de marzo de 2020): 864. http://dx.doi.org/10.3390/w12030864.

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We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.

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44

Goswami, Deepjyoti y Pedro D. Damázio. "A Two-Grid Finite Element Method for Time-Dependent Incompressible Navier-Stokes Equations with Non-Smooth Initial Data". Numerical Mathematics: Theory, Methods and Applications 8, n.º 4 (noviembre de 2015): 549–81. http://dx.doi.org/10.4208/nmtma.2015.m1414.

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AbstractWe analyze here, a two-grid finite element method for the two dimensional time-dependent incompressible Navier-Stokes equations with non-smooth initial data. It involves solving the non-linear Navier-Stokes problem on a coarse grid of size H and solving a Stokes problem on a fine grid of size h, h « H. This method gives optimal convergence for velocity in H1-norm and for pressure in L2-norm. The analysis mainly focuses on the loss of regularity of the solution at t = 0 of the Navier-Stokes equations.

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Ouya, Jules y Arouna Ouedraogo. "Rigorous justification of hydrostatic approximation of compressible fluid flow equations". Gulf Journal of Mathematics 18, n.º 1 (1 de diciembre de 2024): 72–94. https://doi.org/10.56947/gjom.v18i1.2239.

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In this paper, we obtain the 3D compressible primitive equations approximation with gravity by taking the small aspect ratio limit to the Navier-Stokes equations. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations with a pressure law of the form p(ρ) = ρ2 to the compressible primitive equations.

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46

Cliffe, K. A., T. J. Garratt y A. Spence. "A modified Cayley transform for the discretized Navier-Stokes equations". Applications of Mathematics 38, n.º 4 (1993): 281–88. http://dx.doi.org/10.21136/am.1993.104556.

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47

Flandoli, Franco y Marco Romito. "Probabilistic analysis of singularities for the 3D Navier-Stokes equations". Mathematica Bohemica 127, n.º 2 (2002): 211–18. http://dx.doi.org/10.21136/mb.2002.134166.

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48

Friedlander, Susan y Nataša Pavlović. "Remarks concerning modified Navier-Stokes equations". Discrete and Continuous Dynamical Systems 10, n.º 1-2 (octubre de 2003): 269–88. http://dx.doi.org/10.3934/dcds.2004.10.269.

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49

Durmagambetov, Asset A. y Leyla S. Fazilova. "Navier-Stokes Equations—Millennium Prize Problems". Natural Science 07, n.º 02 (2015): 88–99. http://dx.doi.org/10.4236/ns.2015.72010.

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50

Kwean, Hyukjin. "Kwak transformation and Navier-Stokes equations". Communications on Pure and Applied Analysis 3, n.º 3 (junio de 2004): 433–46. http://dx.doi.org/10.3934/cpaa.2004.3.433.

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