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Existence and some limit analysis of stationary solutions for a multi-dimensional bipolar Euler-Poisson system
Derivation and stability study of a rigid lid bilayer model
1. | Laboratoire d'Analyse Numérique et Informatique, Université Gaston Berger, UFR SAT BP 234 Saint-Louis, Sénégal, LAMA, UMR 5127 CNRS, Université de Savoie, 73376 Le Bourget du lac, France |
2. | Laboratoire d'Analyse Numérique et d'Informatique (LANI), Université Gaston Berger, BP 234, Saint-Louis |
References:
[1] |
F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography,, Commun. Math. Sci., 2 (2004), 359.
|
[2] |
E. Audusse, A multilayer Saint-Venant model: derivation and numerical validation,, Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), 189.
doi: 10.3934/dcdsb.2005.5.189. |
[3] |
E. Bruce Pitman and Long Le, A two-fluid model for avalanche and debris flows,, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 363 (2005), 1573.
|
[4] |
B. Di Martino, P. Orenga and M. Peybernes, On a bi-layer shallow water model with rigid-lid hypothesis,, Math. Models Methods Appl. Sci., 15 (2005), 843.
doi: 10.1142/S0218202505000583. |
[5] |
G. Narbona-Reina, J. D. D. Zabsonré, E. D. Fernández-Nieto and D. Bresch, Derivation of a bilayer model for shallow water equations with viscosity. Numerical validation,, CMES Comput. Model. Eng. Sci., 43 (2009), 27.
|
[6] |
B. Di Martino, C. Giacomoni and P. Orenga, Analysis of some shallow water problems with rigid-lid hypothesis,, Math. Models Methods Appl. Sci., 11 (2001), 979.
doi: 10.1142/S0218202501001203. |
[7] |
María Luz Muñoz-Ruiz, Manuel Jesú Castro-Díaz and Carlos Parés, On an one-dimensional bi-layer shallow-water problem,, Nonlinear Anal., 53 (2003), 567.
doi: 10.1016/S0362-546X(02)00137-2. |
[8] |
Philippe Guyenne, David Lannes and Jean-Claude Saut, Well-posedness of the Cauchy problem for models of large amplitude internal waves,, Nonlinearity, 23 (2010), 237.
doi: 10.1088/0951-7715/23/2/003. |
[9] |
D. Bresch and M. Renardy, Well-posedness of two-layer shallow water flow between two horizontal rigid plates,, To appear in nonlinearity, (2011). Google Scholar |
[10] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model,, Comm. Math. Phys., 238 (2003), 211.
|
[11] |
J. Simon, "Équation de Navier-Stokes,'', Cours de DEA 2002-2003 Universit茅 Blaise Pascal Clermont-Ferrand., (): 2002. Google Scholar |
[12] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,'', Dunod, (1969).
|
[13] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equations,, Comm. Partial Differential Equations, 32 (2007), 431.
doi: 10.1080/03605300600857079. |
[14] |
D. Bresch, B. Desjardins and D. Gérard-Varet, On compressible Navier-Stokes equations with density dependent viscosities in bounded domains,, J. Math. Pures Appl. (9), 87 (2007), 227.
doi: 10.1016/j.matpur.2006.10.010. |
[15] |
F. Boyer and P. Fabrie, "Eléments D'analyse pour L'éetude de Quelques Modèles D'écoulements de Fluides Visqueux Incompressibles,'', Mathématiques & Applications (Berlin) [Mathematics & Applications]., ().
|
[16] |
F. Boyer, "Analyse Numérique des edp Elliptiques,'', Cours Master 2 2009 Université Paul Cézanne., (2009). Google Scholar |
show all references
References:
[1] |
F. Bouchut and M. Westdickenberg, Gravity driven shallow water models for arbitrary topography,, Commun. Math. Sci., 2 (2004), 359.
|
[2] |
E. Audusse, A multilayer Saint-Venant model: derivation and numerical validation,, Discrete Contin. Dyn. Syst. Ser. B, 5 (2005), 189.
doi: 10.3934/dcdsb.2005.5.189. |
[3] |
E. Bruce Pitman and Long Le, A two-fluid model for avalanche and debris flows,, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 363 (2005), 1573.
|
[4] |
B. Di Martino, P. Orenga and M. Peybernes, On a bi-layer shallow water model with rigid-lid hypothesis,, Math. Models Methods Appl. Sci., 15 (2005), 843.
doi: 10.1142/S0218202505000583. |
[5] |
G. Narbona-Reina, J. D. D. Zabsonré, E. D. Fernández-Nieto and D. Bresch, Derivation of a bilayer model for shallow water equations with viscosity. Numerical validation,, CMES Comput. Model. Eng. Sci., 43 (2009), 27.
|
[6] |
B. Di Martino, C. Giacomoni and P. Orenga, Analysis of some shallow water problems with rigid-lid hypothesis,, Math. Models Methods Appl. Sci., 11 (2001), 979.
doi: 10.1142/S0218202501001203. |
[7] |
María Luz Muñoz-Ruiz, Manuel Jesú Castro-Díaz and Carlos Parés, On an one-dimensional bi-layer shallow-water problem,, Nonlinear Anal., 53 (2003), 567.
doi: 10.1016/S0362-546X(02)00137-2. |
[8] |
Philippe Guyenne, David Lannes and Jean-Claude Saut, Well-posedness of the Cauchy problem for models of large amplitude internal waves,, Nonlinearity, 23 (2010), 237.
doi: 10.1088/0951-7715/23/2/003. |
[9] |
D. Bresch and M. Renardy, Well-posedness of two-layer shallow water flow between two horizontal rigid plates,, To appear in nonlinearity, (2011). Google Scholar |
[10] |
D. Bresch and B. Desjardins, Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model,, Comm. Math. Phys., 238 (2003), 211.
|
[11] |
J. Simon, "Équation de Navier-Stokes,'', Cours de DEA 2002-2003 Universit茅 Blaise Pascal Clermont-Ferrand., (): 2002. Google Scholar |
[12] |
J.-L. Lions, "Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires,'', Dunod, (1969).
|
[13] |
A. Mellet and A. Vasseur, On the barotropic compressible Navier-Stokes equations,, Comm. Partial Differential Equations, 32 (2007), 431.
doi: 10.1080/03605300600857079. |
[14] |
D. Bresch, B. Desjardins and D. Gérard-Varet, On compressible Navier-Stokes equations with density dependent viscosities in bounded domains,, J. Math. Pures Appl. (9), 87 (2007), 227.
doi: 10.1016/j.matpur.2006.10.010. |
[15] |
F. Boyer and P. Fabrie, "Eléments D'analyse pour L'éetude de Quelques Modèles D'écoulements de Fluides Visqueux Incompressibles,'', Mathématiques & Applications (Berlin) [Mathematics & Applications]., ().
|
[16] |
F. Boyer, "Analyse Numérique des edp Elliptiques,'', Cours Master 2 2009 Université Paul Cézanne., (2009). Google Scholar |
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