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Journal articles on the topic '3D Navier-Stokes'

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Published: 4 June 2021
Last updated: 4 February 2022

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1

Doering, Charles R. "The 3D Navier-Stokes Problem." Annual Review of Fluid Mechanics 41, no. 1 (January 2009): 109–28. http://dx.doi.org/10.1146/annurev.fluid.010908.165218.

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2

Pokorný, Milan, and Piotr B. Mucha. "3D steady compressible Navier--Stokes equations." Discrete & Continuous Dynamical Systems - S 1, no. 1 (2008): 151–63. http://dx.doi.org/10.3934/dcdss.2008.1.151.

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3

RÖCKNER, MICHAEL, and XICHENG ZHANG. "TAMED 3D NAVIER–STOKES EQUATION: EXISTENCE, UNIQUENESS AND REGULARITY." Infinite Dimensional Analysis, Quantum Probability and Related Topics 12, no. 04 (December 2009): 525–49. http://dx.doi.org/10.1142/s0219025709003859.

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In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier–Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier–Stokes equation, then this solution satisfies our tamed equation. Moreover, using this tamed equation we can give a new construction for a suitable weak solution of the classical 3D Navier–Stokes equation introduced in Refs. 16 and 2.
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4

Flandoli, Franco, and Marco Romito. "Probabilistic analysis of singularities for the 3D Navier-Stokes equations." Mathematica Bohemica 127, no. 2 (2002): 211–18. http://dx.doi.org/10.21136/mb.2002.134166.

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5

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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6

Chen, Hui, Daoyuan Fang, and Ting Zhang. "Regularity of 3D axisymmetric Navier-Stokes equations." Discrete & Continuous Dynamical Systems - A 37, no. 4 (2017): 1923–39. http://dx.doi.org/10.3934/dcds.2017081.

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7

Gubinelli, Massimiliano. "Rooted trees for 3D Navier-Stokes equation." Dynamics of Partial Differential Equations 3, no. 2 (2006): 161–72. http://dx.doi.org/10.4310/dpde.2006.v3.n2.a3.

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8

Anh, Cung The, and Nguyen Viet Tuan. "Stabilization of 3D Navier–Stokes–Voigt equations." Georgian Mathematical Journal 27, no. 4 (December 1, 2020): 493–502. http://dx.doi.org/10.1515/gmj-2018-0067.

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AbstractWe consider 3D Navier–Stokes–Voigt equations in smooth bounded domains with homogeneous Dirichlet boundary conditions. First, we study the existence and exponential stability of strong stationary solutions to the problem. Then we show that any unstable steady state can be exponentially stabilized by using either an internal feedback control with a support large enough or a multiplicative Itô noise of sufficient intensity.
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9

Chemin, Jean-Yves, and Ping Zhang. "INHOMOGENEOUS INCOMPRESSIBLE VISCOUS FLOWS WITH SLOWLY VARYING INITIAL DATA." Journal of the Institute of Mathematics of Jussieu 17, no. 5 (November 3, 2016): 1121–72. http://dx.doi.org/10.1017/s1474748016000323.

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The purpose of this paper is to provide a large class of initial data which generates global smooth solution of the 3D inhomogeneous incompressible Navier–Stokes system in the whole space $\mathbb{R}^{3}$. This class of data is based on functions which vary slowly in one direction. The idea is that 2D inhomogeneous Navier–Stokes system with large data is globally well-posed and we construct the 3D approximate solutions by the 2D solutions with a parameter. One of the key point of this study is the investigation of the time decay properties of the solutions to the 2D inhomogeneous Navier–Stokes system. We obtained the same optimal decay estimates as the solutions of 2D homogeneous Navier–Stokes system.
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10

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, no. 4 (1999): 473–517. http://dx.doi.org/10.24033/bsmf.2358.

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11

Iftimie, Dragos, Genevieve Raugel, and George R. Sell. "Navier-Stokes equations in thin 3D domains with Navier boundary conditions." Indiana University Mathematics Journal 56, no. 3 (2007): 1083–156. http://dx.doi.org/10.1512/iumj.2007.56.2834.

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12

Marín-Rubio, Pedro, and James C. Robinson. "Attractors for the Stochastic 3D Navier–Stokes Equations." Stochastics and Dynamics 03, no. 03 (September 2003): 279–97. http://dx.doi.org/10.1142/s0219493703000772.

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In a 1997 paper, Ball defined a generalised semiflow as a means to consider the solutions of equations without (or not known to possess) the property of uniqueness. In particular he used this to show that the 3D Navier–Stokes equations have a global attractor provided that all weak solutions are continuous from (0, ∞) into L2. In this paper we adapt his framework to treat stochastic equations: we introduce a notion of a stochastic generalised semiflow, and then show a similar result to Ball's concerning the attractor of the stochastic 3D Navier–Stokes equations with additive white noise.
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13

Peng, Xuhui, and Rangrang Zhang. "Approximations of stochastic 3D tamed Navier-Stokes equations." Communications on Pure & Applied Analysis 19, no. 12 (2020): 5337–65. http://dx.doi.org/10.3934/cpaa.2020241.

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14

Ma, Kwan Liu, and K. Sikorski. "A distributed 3D Navier-Stokes solver in Express." Energy & Fuels 7, no. 6 (November 1993): 897–901. http://dx.doi.org/10.1021/ef00042a028.

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15

Da Prato, Giuseppe, and Arnaud Debussche. "Ergodicity for the 3D stochastic Navier–Stokes equations." Journal de Mathématiques Pures et Appliquées 82, no. 8 (August 2003): 877–947. http://dx.doi.org/10.1016/s0021-7824(03)00025-4.

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16

Cheskidov, Alexey, Mimi Dai, and Landon Kavlie. "Determining modes for the 3D Navier–Stokes equations." Physica D: Nonlinear Phenomena 374-375 (July 2018): 1–9. http://dx.doi.org/10.1016/j.physd.2017.11.014.

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17

Cutland, Nigel J., and Katarzyna Grzesiak. "Optimal control for 3D stochastic Navier–Stokes equations." Stochastics 77, no. 5 (August 2005): 437–54. http://dx.doi.org/10.1080/17442500500236715.

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18

Sinai, Yakov G. "Diagrammatic approach to the 3D Navier-Stokes system." Russian Mathematical Surveys 60, no. 5 (October 31, 2005): 849–73. http://dx.doi.org/10.1070/rm2005v060n05abeh003735.

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19

Zhou, Yong. "Asymptotic Stability for the 3D Navier–Stokes Equations." Communications in Partial Differential Equations 30, no. 3 (March 2005): 323–33. http://dx.doi.org/10.1081/pde-200037770.

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20

Fan, Jishan, and Hongjun Gao. "Regularity conditions for the 3D Navier-Stokes equations." Quarterly of Applied Mathematics 67, no. 1 (January 8, 2009): 195–99. http://dx.doi.org/10.1090/s0033-569x-09-01119-7.

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21

Ethier, C. Ross, and D. A. Steinman. "Exact fully 3D Navier-Stokes solutions for benchmarking." International Journal for Numerical Methods in Fluids 19, no. 5 (September 15, 1994): 369–75. http://dx.doi.org/10.1002/fld.1650190502.

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22

Awanou, Gerard, and Ming-Jun Lai. "Trivariate spline approximations of 3D Navier-Stokes equations." Mathematics of Computation 74, no. 250 (September 2, 2004): 585–602. http://dx.doi.org/10.1090/s0025-5718-04-01715-6.

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23

Miura, Hideyuki, and Tai-Peng Tsai. "Point Singularities of 3D Stationary Navier–Stokes Flows." Journal of Mathematical Fluid Mechanics 14, no. 1 (December 14, 2010): 33–41. http://dx.doi.org/10.1007/s00021-010-0046-6.

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24

Hong, Youngjoon, and Djoko Wirosoetisno. "Timestepping schemes for the 3d Navier–Stokes equations." Applied Numerical Mathematics 96 (October 2015): 153–64. http://dx.doi.org/10.1016/j.apnum.2015.05.006.

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25

Iftimie, Dragoş. "Les équations de navier-stokes 3D vues comme une perturbation des équations de navier-stokes 2D." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 324, no. 3 (February 1997): 271–74. http://dx.doi.org/10.1016/s0764-4442(99)80359-0.

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26

Wang, Wen-Juan, and Yan Jia. "The Asymptotic Stability of the Generalized 3D Navier-Stokes Equations." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/321427.

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We study the stability issue of the generalized 3D Navier-Stokes equations. It is shown that if the weak solutionuof the Navier-Stokes equations lies in the regular class∇u∈Lp(0,∞;Bq,∞0(ℝ3)),(2α/p)+(3/q)=2α,2<q<∞,0<α<1, then every weak solutionv(x,t)of the perturbed system converges asymptotically tou(x,t)asvt-utL2→0,t→∞.
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27

Cheng, Jian, Xiaodong Liu, Tiegang Liu, and Hong Luo. "A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids." Communications in Computational Physics 21, no. 5 (March 27, 2017): 1231–57. http://dx.doi.org/10.4208/cicp.oa-2016-0090.

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AbstractA parallel, high-order direct Discontinuous Galerkin (DDG) method has been developed for solving the three dimensional compressible Navier-Stokes equations on 3D hybrid grids. The most distinguishing and attractive feature of DDG method lies in its simplicity in formulation and efficiency in computational cost. The formulation of the DDG discretization for 3D Navier-Stokes equations is detailed studied and the definition of characteristic length is also carefully examined and evaluated based on 3D hybrid grids. Accuracy studies are performed to numerically verify the order of accuracy using flow problems with analytical solutions. The capability in handling curved boundary geometry is also demonstrated. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results obtained indicate that the DDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations.
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28

Kang, Ensil, and Jihoon Lee. "Notes on the Global Well-Posedness for the Maxwell-Navier-Stokes System." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/402793.

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Masmoudi (2010) obtained global well-posedness for 2D Maxwell-Navier-Stokes system. In this paper, we reprove global existence of regular solutions to the 2D system by using energy estimates and Brezis-Gallouet inequality. Also we obtain a blow-up criterion for solutions to 3D Maxwell-Navier-Stokes system.
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29

Hu, Changbing. "Navier–Stokes equations in 3D thin domains with Navier friction boundary condition." Journal of Differential Equations 236, no. 1 (May 2007): 133–63. http://dx.doi.org/10.1016/j.jde.2007.02.001.

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30

Wang, Aiwen, Xin Zhao, Peihua Qin, and Dongxiu Xie. "An Oseen Two-Level Stabilized Mixed Finite-Element Method for the 2D/3D Stationary Navier-Stokes Equations." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/520818.

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We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e.,Q1−P0andP1−P0). Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh sizeH, a large general Stokes equation on the fine mesh with mesh sizeh=O(H)2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph) with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh sizeh. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.
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31

Gibbon, John D., Anupam Gupta, Nairita Pal, and Rahul Pandit. "The role of BKM-type theorems in 3D Euler, Navier–Stokes and Cahn–Hilliard–Navier–Stokes analysis." Physica D: Nonlinear Phenomena 376-377 (August 2018): 60–68. http://dx.doi.org/10.1016/j.physd.2017.11.007.

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32

Li, Shihu, Wei Liu, and Yingchao Xie. "Ergodicity of 3D Leray-α model with fractional dissipation and degenerate stochastic forcing." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 01 (March 2019): 1950002. http://dx.doi.org/10.1142/s0219025719500024.

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By using the asymptotic coupling method, the asymptotic log-Harnack inequality is established for the transition semigroup associated to the 3D Leray-[Formula: see text] model with fractional dissipation driven by highly degenerate noise. As applications, we derive the asymptotic strong Feller property and ergodicity for the stochastic 3D Leray-[Formula: see text] model with fractional dissipation, which is the stochastic 3D Navier–Stokes equation regularized through a smoothing kernel of order [Formula: see text] in the nonlinear term and a [Formula: see text]-fractional Laplacian. The main results can be applied to the classical stochastic 3D Leray-[Formula: see text] model ([Formula: see text]), stochastic 3D hyperviscous Navier–Stokes equation ([Formula: see text]) and stochastic 3D critical Leray-[Formula: see text] model ([Formula: see text]).
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33

Jeong, Hyosuk. "REGULARITY OF 3D NAVIER-STOKES EQUATIONS WITH SPECTRAL DECOMPOSITION." Honam Mathematical Journal 38, no. 3 (September 25, 2016): 583–92. http://dx.doi.org/10.5831/hmj.2016.38.3.583.

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34

Roh, Jaiok. "Spatial stability of 3D exterior stationary Navier–Stokes flows." Journal of Mathematical Analysis and Applications 389, no. 2 (May 2012): 1139–58. http://dx.doi.org/10.1016/j.jmaa.2011.12.053.

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35

Vasseur, Alexis. "Higher derivatives estimate for the 3D Navier–Stokes equation." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 27, no. 5 (September 2010): 1189–204. http://dx.doi.org/10.1016/j.anihpc.2010.05.002.

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36

Rodrigues, Sérgio S. "Local exact boundary controllability of 3D Navier–Stokes equations." Nonlinear Analysis: Theory, Methods & Applications 95 (January 2014): 175–90. http://dx.doi.org/10.1016/j.na.2013.09.003.

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37

Bae, Hantaek, and Marco Cannone. "Log-Lipschitz regularity of the 3D Navier–Stokes equations." Nonlinear Analysis: Theory, Methods & Applications 135 (April 2016): 223–35. http://dx.doi.org/10.1016/j.na.2016.01.014.

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38

Zhang, Xicheng. "A tamed 3D Navier–Stokes equation in uniform -domains." Nonlinear Analysis: Theory, Methods & Applications 71, no. 7-8 (October 2009): 3093–112. http://dx.doi.org/10.1016/j.na.2009.01.221.

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39

Gazzola, F. "An Attractor for a 3D Navier-Stokes Type Equation." Zeitschrift für Analysis und ihre Anwendungen 14, no. 3 (1995): 509–22. http://dx.doi.org/10.4171/zaa/636.

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40

Riemann, J., M. Borchardt, R. Schneider, A. Mutzke, T. D. Rognlien, and M. Umansky. "Navier-Stokes Neutral and Plasma Fluid Modelling in 3D." Contributions to Plasma Physics 44, no. 13 (April 2004): 35–38. http://dx.doi.org/10.1002/ctpp.200410005.

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41

Boukrouche, Mahdi, Imane Boussetouan, and Laetitia Paoli. "Unsteady 3D-Navier–Stokes system with Tresca’s friction law." Quarterly of Applied Mathematics 78, no. 3 (November 22, 2019): 525–43. http://dx.doi.org/10.1090/qam/1563.

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42

Avrinl, J., A. Babinl, A. Mahalov, and B. Nicolaenko. "On regularity of solutions of 3D navier-stokes equations." Applicable Analysis 71, no. 1-4 (December 1998): 197–214. http://dx.doi.org/10.1080/00036819908840713.

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43

Cheskidov, Alexey, and Landon Kavlie. "Degenerate Pullback Attractors for the 3D Navier–Stokes Equations." Journal of Mathematical Fluid Mechanics 17, no. 3 (July 11, 2015): 411–21. http://dx.doi.org/10.1007/s00021-015-0214-9.

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44

Flandoli, Franco, and Marco Romito. "Markov selections for the 3D stochastic Navier–Stokes equations." Probability Theory and Related Fields 140, no. 3-4 (March 31, 2007): 407–58. http://dx.doi.org/10.1007/s00440-007-0069-y.

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45

Gibbon, J. D., and Charles R. Doering. "Intermittency and Regularity Issues in 3D Navier-Stokes Turbulence." Archive for Rational Mechanics and Analysis 177, no. 1 (June 1, 2005): 115–50. http://dx.doi.org/10.1007/s00205-005-0382-5.

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46

Röckner, Michael, Tusheng Zhang, and Xicheng Zhang. "Large Deviations for Stochastic Tamed 3D Navier-Stokes Equations." Applied Mathematics and Optimization 61, no. 2 (September 15, 2009): 267–85. http://dx.doi.org/10.1007/s00245-009-9089-6.

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47

Odasso, Cyril. "Exponential Mixing for the 3D Stochastic Navier–Stokes Equations." Communications in Mathematical Physics 270, no. 1 (December 1, 2006): 109–39. http://dx.doi.org/10.1007/s00220-006-0156-4.

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48

Pan, Xinghong. "A Regularity Condition of 3d Axisymmetric Navier-Stokes Equations." Acta Applicandae Mathematicae 150, no. 1 (April 6, 2017): 103–9. http://dx.doi.org/10.1007/s10440-017-0096-3.

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49

Cheskidov, A., and C. Foias. "On global attractors of the 3D Navier–Stokes equations." Journal of Differential Equations 231, no. 2 (December 2006): 714–54. http://dx.doi.org/10.1016/j.jde.2006.08.021.

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50

Shen, Wen Zhong, and Jens Nørkær Sørensen. "Quasi-3D Navier–Stokes Model for a Rotating Airfoil." Journal of Computational Physics 150, no. 2 (April 1999): 518–48. http://dx.doi.org/10.1006/jcph.1999.6203.

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