Relevant bibliographies by topics / Local well-posedness

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Local well-posedness'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Local well-posedness"

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Willison, Steven. "Local well-posedness in Lovelock gravity." Classical and Quantum Gravity 32, no. 2 (December 19, 2014): 022001. http://dx.doi.org/10.1088/0264-9381/32/2/022001.

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Isaza, Pedro, and Jorge Mejía. "Local well-posedness and quantitative ill-posedness for the Ostrovsky equation." Nonlinear Analysis: Theory, Methods & Applications 70, no. 6 (March 2009): 2306–16. http://dx.doi.org/10.1016/j.na.2008.03.010.

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CHEN, Zeqian. "Local Well-posedness for Gross-Pitaevskii Hierarchies." Acta Analysis Functionalis Applicata 15, no. 4 (2013): 291. http://dx.doi.org/10.3724/sp.j.1160.2013.00291.

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Kishimoto, Nobu. "Unconditional local well-posedness for periodic NLS." Journal of Differential Equations 274 (February 2021): 766–87. http://dx.doi.org/10.1016/j.jde.2020.10.025.

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Hille, Sander C. "Local Well-posedness of Kinetic Chemotaxis Models." Journal of Evolution Equations 8, no. 3 (May 20, 2008): 423–48. http://dx.doi.org/10.1007/s00028-008-0358-7.

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Shatah, Jalal, and Chongchun Zeng. "Local Well-Posedness for Fluid Interface Problems." Archive for Rational Mechanics and Analysis 199, no. 2 (June 30, 2010): 653–705. http://dx.doi.org/10.1007/s00205-010-0335-5.

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Racke, Reinhard, and Jürgen Saal. "Hyperbolic Navier-Stokes equations I: Local well-posedness." Evolution Equations and Control Theory 1, no. 1 (March 2012): 195–215. http://dx.doi.org/10.3934/eect.2012.1.195.

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Liu, Yongqin, and Weike Wang. "Local well-posedness of a new integrable equation." Nonlinear Analysis: Theory, Methods & Applications 64, no. 11 (June 2006): 2516–26. http://dx.doi.org/10.1016/j.na.2005.08.030.

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Zhong, Xin, Xing-Ping Wu, and Chun-Lei Tang. "Local well-posedness for the homogeneous Euler equations." Nonlinear Analysis: Theory, Methods & Applications 74, no. 11 (July 2011): 3829–48. http://dx.doi.org/10.1016/j.na.2011.03.037.

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Dörfler, Willy, Hannes Gerner, and Roland Schnaubelt. "Local well-posedness of a quasilinear wave equation." Applicable Analysis 95, no. 9 (September 23, 2015): 2110–23. http://dx.doi.org/10.1080/00036811.2015.1089236.

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Dissertations / Theses on the topic "Local well-posedness"

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Candy, Timothy Lars. "Local and global well-posedness for nonlinear Dirac type equations." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7962.

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We investigate the local and global well-posedness of a variety of nonlinear Dirac type equations with null structure on R1+1. In particular, we prove global existence in L2 for a nonlinear Dirac equation known as the Thirring model. Local existence in Hs for s > 0, and global existence for s > 1/2 , has recently been proven by Selberg-Tesfahun where they used Xs,b spaces together with a type of null form estimate. In contrast, motivated by the recent work of Machihara-Nakanishi-Tsugawa, we prove local existence in the scale invariant class L2 by using null coordinates. Moreover, again using null coordinates, we prove almost optimal local wellposedness for the Chern-Simons-Dirac equation which extends recent work of Huh. To prove global well-posedness for the Thirring model, we introduce a decomposition which shows the solution is linear (up to gauge transforms in U(1)), with an error term that can be controlled in L∞. This decomposition is also applied to prove global existence for the Chern-Simons-Dirac equation. This thesis also contains a study of bilinear estimates in Xs,b± (R2) spaces. These estimates are often used in the theory of nonlinear Dirac equations on R1+1. We prove estimates that are optimal up to endpoints by using dyadic decomposition together with some simplifications due to Tao. As an application, by using the I-method of Colliander-Keel-Staffilani-Takaoka-Tao, we extend the work of Tesfahun on global existence below the charge class for the Dirac-Klein- Gordon equation on R1+1. The final result contained in this thesis concerns the space-time Monopole equation. Recent work of Czubak showed that the space-time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in Hs(R2) for s > 1/4 . Here we show that the Monopole equation has null structure in Lorenz gauge, and use this to prove local well-posedness for large initial data in Hs(R2) with s > 1/4.
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Moşincat, Răzvan Octavian. "Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33244.

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This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial data in two settings: (i) on the torus (namely with the periodic boundary condition) and (ii) on the real line. Our first main goal is to study the global-in-time behaviour of solutions to DNLS in the periodic setting, where global well-posedness is known to hold under a small mass assumption. In Chapter 2, we relax the smallness assumption on the mass and establish global well-posedness of DNLS for smooth initial data. In Chapter 3, we then extend this result for rougher initial data. In particular, we employ the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao and show the global well-posedness of the periodic DNLS at the end-point regularity. In the implementation of the I-method, we apply normal form reductions to construct higher order modified energy functionals. In Chapter 4, we turn our attention to the uniqueness of solutions to DNLS on the real line. By using an infinite iteration of normal form reductions introduced by Guo, Kwon, and Oh in the context of one-dimensional cubic NLS on the torus, we construct solutions to DNLS without using any auxiliary function space. As a result, we prove the unconditional uniqueness of solutions to DNLS on the real line in an almost end-point regularity.
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Kalantarova, Habiba [Verfasser]. "Local Smoothing and Well-Posedness Results for KP-II Type Equations / Habiba Kalantarova." Bonn : Universitäts- und Landesbibliothek Bonn, 2015. http://d-nb.info/107728957X/34.

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Bürger, Steven. "About an autoconvolution problem arising in ultrashort laser pulse characterization." Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-154367.

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We are investigating a kernel-based autoconvolution problem, which has its origin in the physics of ultra short laser pulses. The task in this problem is to reconstruct a complex-valued function $x$ on a finite interval from measurements of its absolute value and a kernel-based autoconvolution of the form [[F(x)](s)=int k(s,t)x(s-t)x(t)de t.] This problem has not been studied in the literature. One reason might be that one has more information than in the classical autoconvolution case, where only the right hand side is available. Nevertheless we show that ill posedness phenomena may occur. We also propose an algorithm to solve the problem numerically and demonstrate its performance with artificial data. Since the algorithm fails to produce good results with real data and we suspect that the data for $|F(x)|$ are not dependable we also consider the whole problem with only $arg(F(x))$ given instead of $F(x)$.
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Terzi, Marina. "LOCAL WELL POSEDNESS, REGULARITY, AND STABILITY FOR THE TIME-FRACTIONAL BURGERS PIDES ON THE WHOLE ONE, TWO, AND THREE DIMENSIONAL SPACES." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1595780869268506.

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Montealegre, Scott Juan. "Initial value problem for a coupled system of Kadomtsev-Petviashvili II equations in Sobolev spaces of negative indices." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95255.

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Sousa, Alexandre do Nascimento Oliveira. "Equações de Navier-Stokes: o problema de um milhão de dólares sob o ponto de vista da continuação de soluções." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-16112017-160410/.

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Neste trabalho consideramos o problema de Navier-Stokes em RN
ut = Δu — ∇π + f (t) — (u .∇)u,   x∈ Ω
div(u) = 0,    x ∈ Ω
u = 0,    x ∈ ∂ Ω
u(0, x) = u0 (x), onde u0 ∈ LN (Ω)N e Ω é um subconjunto aberto, limitado e suave de RN. Provamos que o problema acima é localmente bem colocado e fornecemos condições para obter que estas soluções existem para todo t ≥ 0. Utilizamos técnicas de equações parabólicas semilineares considerando não linearidades com crescimento crítico desenvolvidas em (ARRIETA; CARVALHO, 1999).
In this work we we consider the Navier-Stokes problem on RN
ut = Δu — ∇π + f (t) — (u .∇)u,   x∈ Ω
div(u) = 0,    x ∈ Ω
u = 0,    x ∈ ∂ Ω
u(0, x) = u0 (x), where u0 ∈ LN (Ω)N and Ω is an open, bounded and smooth subset of RN. We prove that the above problem is locally well posed and give conditions to obtain that these solutions exist for all t ≥ 0. We used techniques of semilinear parabolic equations considering nonlinearities with critical grouth developed in (ARRIETA; CARVALHO, 1999).
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Bürger, Steven, and Bernd Hofmann. "About a deficit in low order convergence rates on the example of autoconvolution." Universitätsbibliothek Chemnitz, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-130630.

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We revisit in L2-spaces the autoconvolution equation x ∗ x = y with solutions which are real-valued or complex-valued functions x(t) defined on a finite real interval, say t ∈ [0,1]. Such operator equations of quadratic type occur in physics of spectra, in optics and in stochastics, often as part of a more complex task. Because of their weak nonlinearity deautoconvolution problems are not seen as difficult and hence little attention is paid to them wrongly. In this paper, we will indicate on the example of autoconvolution a deficit in low order convergence rates for regularized solutions of nonlinear ill-posed operator equations F(x)=y with solutions x† in a Hilbert space setting. So for the real-valued version of the deautoconvolution problem, which is locally ill-posed everywhere, the classical convergence rate theory developed for the Tikhonov regularization of nonlinear ill-posed problems reaches its limits if standard source conditions using the range of F (x† )∗ fail. On the other hand, convergence rate results based on Hölder source conditions with small Hölder exponent and logarithmic source conditions or on the method of approximate source conditions are not applicable since qualified nonlinearity conditions are required which cannot be shown for the autoconvolution case according to current knowledge. We also discuss the complex-valued version of autoconvolution with full data on [0,2] and see that ill-posedness must be expected if unbounded amplitude functions are admissible. As a new detail, we present situations of local well-posedness if the domain of the autoconvolution operator is restricted to complex L2-functions with a fixed and uniformly bounded modulus function.
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Santos, Carlos Alberto Silva dos. "O problema de Cauchy para as equações KdV e mKdV." Universidade Federal de Alagoas, 2009. http://repositorio.ufal.br/handle/riufal/1040.

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In this work we will demonstrate that the Cauchy problem associated with the Korteweg-de Vries equation, denoted by KdV, and Korteweg-de Vries modified equation, denoted by mKdV, with initial data in the space of Sobolev Hs(|R), is locally well-posed on Hs(|R), with s>3/4 for KdV and s≥1/4 for mKdV, where the notion of well-posedness includes existence, uniqueness, persistence property of solution and continuous dependence of solution with respect to the initial data. This result is based on the works of Kenig, Ponce and Vega. The technique used to obtain these results is based on fixed point Banach theorem combined with the regularizantes effects of the group associated with the linear part.
Fundação de Amparo a Pesquisa do Estado de Alagoas
Neste trabalho demonstraremos que o problema de Cauchy associado as equações de Korteweg-de Vries, denotada por KdV, e de Korteweg-de Vries modificada, denotada por mKdV, com dado inicial no espaço de Sobolev Hs(|R), é bem posto localmente em Hs(|R), com s>3/4 para a KdV e s≥1/4 para a mKdV, onde a noção de boa postura inclui a existência, unicidade, a propriedade de persistência da solução e dependência contínua da solução com relação ao dado inicial. Este resultado é baseado nos trabalhos de Kenig, Ponce e Vega. A técnica utilizada para obter tais resultados se baseia no Teorema do Ponto Fixo de Banach combinada com os efeitos regularizantes do grupo associado com a parte linear.
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Montealegre, Scott Juan. "Problema de Cauchy para un Sistema de Tipo Benjamin-Bona-Mahony." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95533.

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It is proved that the initial value problem for a system of two Benjamin-Bona-Mahony equations coupled through both dispersive and nonlinear terms is locally and globally well posed in the Soboloev spaces Hs ×Hs with s ≥ 0
Dado el problema de valor inicial para un sistema de dos ecuaciones de Benjamin-Bona-Mahony (BBM) acopladas a través de los términos dispersivos y no lineales, se demuestra que está bien colocado localmente y globalmente en los espacios Hs × Hs con s≥0.
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Book chapters on the topic "Local well-posedness"

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Prüss, Jan, and Gieri Simonett. "Local Well-Posedness and Regularity." In Moving Interfaces and Quasilinear Parabolic Evolution Equations, 419–50. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27698-4_9.

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Shvydkoy, Roman. "Local Well-Posedness and Continuation Criteria." In Nečas Center Series, 121–41. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68147-0_7.

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Bellettini, Giovanni. "Local well-posedness: the approach of Evans and Spruck." In Lecture Notes on Mean Curvature Flow, Barriers and Singular Perturbations, 103–26. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-429-8_7.

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Ehrnström, Mats, Joachim Escher, and Long Pei. "A Note on the Local Well-Posedness for the Whitham Equation." In Elliptic and Parabolic Equations, 63–75. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12547-3_3.

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Carvajal, Xavier, and Mahendra Panthee. "A Note on Local Well-Posedness of Generalized KdV Type Equations with Dissipative Perturbations." In Springer Proceedings in Mathematics & Statistics, 85–100. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66839-0_4.

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Ogawa, Takayoshi, and Yuuki Yamane. "Local Well-Posedness for the Cauchy Problem to Nonlinear Heat Equations of Fujita Type in Nearly Critical Besov Space." In Springer Proceedings in Mathematics & Statistics, 215–39. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66764-5_10.

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Chaichenets, Leonid, Dirk Hundertmark, Peer Christian Kunstmann, and Nikolaos Pattakos. "Local Well-Posedness for the Nonlinear Schrödinger Equation in the Intersection of Modulation Spaces $$M_{p, q}^s({\mathbb {R}}^d) \cap M_{\infty , 1}({\mathbb {R}}^d)$$." In Trends in Mathematics, 89–107. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47174-3_6.

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Chaichenets, Leonid, Dirk Hundertmark, Peer Christian Kunstmann, and Nikolaos Pattakos. "Correction to: Local Well-Posedness for the Nonlinear Schrödinger Equation in the Intersection of Modulation Spaces $$M_{p, q}^s({\mathbb {R}}^d) \cap M_{\infty , 1}({\mathbb {R}}^d)$$." In Trends in Mathematics, C1. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47174-3_20.

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"5. Local well-posedness." In Stochastically Forced Compressible Fluid Flows, 187–216. De Gruyter, 2018. http://dx.doi.org/10.1515/9783110492552-005.

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"The local well-posedness theory." In Series in Applied and Computational Mathematics, 141–44. WORLD SCIENTIFIC, 2014. http://dx.doi.org/10.1142/9789814641630_0011.

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Conference papers on the topic "Local well-posedness"

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ZHANG, HUA, and HONG-FENG WU. "LOCAL WELL-POSEDNESS FOR THE FOURTH ORDER SCHRÖDINGER EQUATION." In Proceedings of the Third International Conference. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814327862_0008.

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Ferreira, Lucas C. F., and Juliana C. Precioso. "Local well-posedness for 3D micropolar uid system in Besov-Morrey spaces." In XXXV CNMAC - Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2015. http://dx.doi.org/10.5540/03.2015.003.01.0006.

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Dündar, Nurhan, and Necat Polat. "On the local well-posedness of a generalized two-component Camassa-Holm system." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930523.

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Shuo, Wang, Ding Yunhua, and Xu Runzhang. "Local well-posedness for nonlinear Klein-Gordon equation with weak and strong damping terms." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756618.

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Blokhin, A. M., and D. L. Tkachev. "Local well-posedness in the problem of ow about in nite plane wedge with inviscous non-heat-conducting gas." In 2017 Days on Diffraction (DD). IEEE, 2017. http://dx.doi.org/10.1109/dd.2017.8167997.

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Robens, Sebastian, Peter Jeschke, Christian Frey, Edmund Kügeler, Arianna Bosco, and Thomas Breuer. "Adaption of Giles Non-Local Non-Reflecting Boundary Conditions for a Cell-Centered Solver for Turbomachinery Applications." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94957.

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In contrast to external flow aerodynamics, where one-dimensional Riemann boundary conditions can be applied far up- and downstream, the handling of non-reflecting boundary conditions for turbomachinery applications poses a greater challenge due to small axial gaps normally encountered. For boundaries exposed to non-uniform flow in the vicinity of blade rows, the quality of the simulation is greatly influenced by the underlying non-reflecting boundary condition and its implementation. This paper deals with the adaptation of Giles’ well-known exact non-local boundary conditions for two-dimensional steady flows to a cell-centered solver specifically developed for turbomachinery applications. It is shown that directly applying the theory originally formulated for a cell-vertex scheme to a cell-centered solver may yield an ill-posed problem due to the necessity of having to reconstruct boundary face values before actually applying the exact non-reflecting theory. In order to ensure well-posedness, Giles’ original approach is adapted for cell-centered schemes with a physically motivated reconstruction of the boundary face values, while still maintaining the non-reflecting boundary conditions. The extension is formulated within the original framework of determining the circumferential distribution of one-dimensional characteristics on the boundary. It is shown that, due to approximations in the one-dimensional characteristic reconstruction of boundary face values, the new approach can only be exact in the limiting case of cells with a vanishing width in the direction normal to the boundary if a one-dimensional characteristic reconstruction of boundary face values is used. To overcome the dependency on the width of the last cell, the new boundary condition is expressed explicitly in terms of a two-dimensional modal decomposition of the flow field. In this formulation, vanishing modal amplitudes for all incoming two-dimensional modes can easily be accomplished for a converged solution. Hence we are able to ensure perfectly non-reflecting boundary conditions under the same conditions as the original approach. The improvements of the new method are demonstrated for both a subsonic turbine and a transonic compressor test case.
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Vaidheeswaran, Avinash, William D. Fullmer, Krishna Chetty, Raul G. Marino, and Martin Lopez de Bertodano. "Stability Analysis of Chaotic Wavy Stratified Fluid-Fluid Flow With the 1D Fixed-Flux Two-Fluid Model." In ASME 2016 Fluids Engineering Division Summer Meeting collocated with the ASME 2016 Heat Transfer Summer Conference and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/fedsm2016-1058.

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The one-dimensional fixed-flux two-fluid model (TFM) is used to analyze the stability of the wavy interface in a slightly inclined pipe geometry. The model is reduced from the complete 1-D TFM, assuming a constant total volumetric flux, which resembles the equations of shallow water theory (SWT). From the point of view of two-phase flow physics, the Kelvin-Helmholtz instability, resulting from the relative motion between the phases, is still preserved after the simplification. Hence, the numerical fixed-flux TFM proves to be an effective tool to analyze local features of two-phase flow, in particular the chaotic behavior of the interface. Experiments on smooth- and wavy-stratified flows with water and gasoline were performed to understand the interface dynamics. The mathematical behavior concerning the well-posedness and stability of the fixed-flux TFM is first addressed using linear stability theory. The findings from the linear stability analysis are also important in developing the eigenvalue based donoring flux-limiter scheme used in the numerical simulations. The stability analysis is extended past the linear theory using nonlinear simulations to estimate the Largest Lyapunov Exponent which confirms the non-linear boundedness of the fixed-flux TFM. Furthermore, the numerical model is shown to be convergent using the power spectra in Fourier space. The nonlinear results are validated with the experimental data. The chaotic behavior of the interface from the numerical predictions is similar to the results from the experiments.
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