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A multilayer Saint-Venant model: Derivation and numerical validation
1. | INRIA Rocquencourt, Domaine de Voluceau BP 105, 78153 Le Chesnay, France |
[1] |
Jean-Frédéric Gerbeau, Benoit Perthame. Derivation of viscous Saint-Venant system for laminar shallow water; Numerical validation. Discrete and Continuous Dynamical Systems - B, 2001, 1 (1) : 89-102. doi: 10.3934/dcdsb.2001.1.89 |
[2] |
Marie-Odile Bristeau, Jacques Sainte-Marie. Derivation of a non-hydrostatic shallow water model; Comparison with Saint-Venant and Boussinesq systems. Discrete and Continuous Dynamical Systems - B, 2008, 10 (4) : 733-759. doi: 10.3934/dcdsb.2008.10.733 |
[3] |
Emmanuel Audusse, Fayssal Benkhaldoun, Jacques Sainte-Marie, Mohammed Seaid. Multilayer Saint-Venant equations over movable beds. Discrete and Continuous Dynamical Systems - B, 2011, 15 (4) : 917-934. doi: 10.3934/dcdsb.2011.15.917 |
[4] |
Hassen Arfaoui, Faker Ben Belgacem, Henda El Fekih, Jean-Pierre Raymond. Boundary stabilizability of the linearized viscous Saint-Venant system. Discrete and Continuous Dynamical Systems - B, 2011, 15 (3) : 491-511. doi: 10.3934/dcdsb.2011.15.491 |
[5] |
Georges Bastin, Jean-Michel Coron, Brigitte d'Andréa-Novel. On Lyapunov stability of linearised Saint-Venant equations for a sloping channel. Networks and Heterogeneous Media, 2009, 4 (2) : 177-187. doi: 10.3934/nhm.2009.4.177 |
[6] |
Xulong Qin, Zheng-An Yao, Hongxing Zhao. One dimensional compressible Navier-Stokes equations with density-dependent viscosity and free boundaries. Communications on Pure and Applied Analysis, 2008, 7 (2) : 373-381. doi: 10.3934/cpaa.2008.7.373 |
[7] |
Xulong Qin, Zheng-An Yao. Global solutions of the free boundary problem for the compressible Navier-Stokes equations with density-dependent viscosity. Communications on Pure and Applied Analysis, 2010, 9 (4) : 1041-1052. doi: 10.3934/cpaa.2010.9.1041 |
[8] |
Yoshihiro Shibata. Local well-posedness of free surface problems for the Navier-Stokes equations in a general domain. Discrete and Continuous Dynamical Systems - S, 2016, 9 (1) : 315-342. doi: 10.3934/dcdss.2016.9.315 |
[9] |
Wenjun Wang, Lei Yao. Spherically symmetric Navier-Stokes equations with degenerate viscosity coefficients and vacuum. Communications on Pure and Applied Analysis, 2010, 9 (2) : 459-481. doi: 10.3934/cpaa.2010.9.459 |
[10] |
Yann Brenier. Approximation of a simple Navier-Stokes model by monotonic rearrangement. Discrete and Continuous Dynamical Systems, 2014, 34 (4) : 1285-1300. doi: 10.3934/dcds.2014.34.1285 |
[11] |
Hantaek Bae. Solvability of the free boundary value problem of the Navier-Stokes equations. Discrete and Continuous Dynamical Systems, 2011, 29 (3) : 769-801. doi: 10.3934/dcds.2011.29.769 |
[12] |
Roberta Bianchini, Roberto Natalini. Convergence of a vector-BGK approximation for the incompressible Navier-Stokes equations. Kinetic and Related Models, 2019, 12 (1) : 133-158. doi: 10.3934/krm.2019006 |
[13] |
Michele Coti Zelati. Remarks on the approximation of the Navier-Stokes equations via the implicit Euler scheme. Communications on Pure and Applied Analysis, 2013, 12 (6) : 2829-2838. doi: 10.3934/cpaa.2013.12.2829 |
[14] |
Zhigang Wang. Vanishing viscosity limit of the rotating shallow water equations with far field vacuum. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 311-328. doi: 10.3934/dcds.2018015 |
[15] |
Chengchun Hao. Cauchy problem for viscous shallow water equations with surface tension. Discrete and Continuous Dynamical Systems - B, 2010, 13 (3) : 593-608. doi: 10.3934/dcdsb.2010.13.593 |
[16] |
J. Huang, Marius Paicu. Decay estimates of global solution to 2D incompressible Navier-Stokes equations with variable viscosity. Discrete and Continuous Dynamical Systems, 2014, 34 (11) : 4647-4669. doi: 10.3934/dcds.2014.34.4647 |
[17] |
Ping Chen, Ting Zhang. A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients. Communications on Pure and Applied Analysis, 2008, 7 (4) : 987-1016. doi: 10.3934/cpaa.2008.7.987 |
[18] |
Yuming Qin, Lan Huang, Shuxian Deng, Zhiyong Ma, Xiaoke Su, Xinguang Yang. Interior regularity of the compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum. Discrete and Continuous Dynamical Systems - S, 2009, 2 (1) : 163-192. doi: 10.3934/dcdss.2009.2.163 |
[19] |
Pavel I. Plotnikov, Jan Sokolowski. Compressible Navier-Stokes equations. Conference Publications, 2009, 2009 (Special) : 602-611. doi: 10.3934/proc.2009.2009.602 |
[20] |
Jan W. Cholewa, Tomasz Dlotko. Fractional Navier-Stokes equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (8) : 2967-2988. doi: 10.3934/dcdsb.2017149 |
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