Comptes Rendus
no. 7-8
Partial Differential Equations
Existence of a global weak solution to Compressible Primitive Equations
[Existence dʼune solution faible pour un modèle dʼÉquations Primitives Compressibles]

Présenté par : the Editorial Board

Mehmet Ersoy1, 2, 3 ; Timack Ngom2, 4
1 Institut de mathématique de Toulon (IMATH), université du Sud Toulon-Var, avenue G. Pompidou, BP 56, 83162 La Valette du Var, France
2 Laboratoire de mathématiques (LAMA), université de Savoie, 73376 Le Bourget du Lac, France
3 Basque Center for Applied Mathematics (BCAM), Bizkaia Technology Park 500, 48160 Derio, Basque Country, Spain
4 Laboratoire dʼanalyse numérique et informatique (LANI), université Gaston Berger de Saint-Louis, UFR SAT, BP 234, Saint-Louis, Senegal
Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 379-382.

In this Note, we show a global weak existence result for a two dimensional Compressible Primitive Equations for atmosphere dynamics modeling.

Dans cette Note, on montre un résultat dʼexistence de solutions faibles globale en temps pour un modèle dʼÉquations Primitives Compressibles en dimension deux pour la dynamique de lʼatmosphère.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.04.013

Mehmet Ersoy 1, 2, 3 ; Timack Ngom 2, 4

1 Institut de mathématique de Toulon (IMATH), université du Sud Toulon-Var, avenue G. Pompidou, BP 56, 83162 La Valette du Var, France
2 Laboratoire de mathématiques (LAMA), université de Savoie, 73376 Le Bourget du Lac, France
3 Basque Center for Applied Mathematics (BCAM), Bizkaia Technology Park 500, 48160 Derio, Basque Country, Spain
4 Laboratoire dʼanalyse numérique et informatique (LANI), université Gaston Berger de Saint-Louis, UFR SAT, BP 234, Saint-Louis, Senegal 
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Mehmet Ersoy; Timack Ngom. Existence of a global weak solution to Compressible Primitive Equations. Comptes Rendus. Mathématique, Volume 350 (2012) no. 7-8, pp. 379-382. doi : 10.1016/j.crma.2012.04.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.013/

[1] M. Ersoy; T. Ngom; M. Sy Compressible primitive equations: formal derivation and stability of weak solutions, Nonlinearity, Volume 24 (2011) no. 1, pp. 79-96

[2] B.V. Gatapov; A.V. Kazhikhov Existence of a global solution to one model problem of atmosphere dynamics, Sibirsk. Mat. Zh., Volume 1011 (2005), pp. 1020-1722

[3] J.-F. Gerbeau; B. Perthame Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation, Discrete Contin. Dyn. Syst. Ser. B, Volume 1 (2001) no. 1, pp. 89-102

[4] J.L. Lions; R. Temam; S. Wang New formulations for the primitive equations for the atmosphere and applications, Nonlinearity, Volume 5 (1992), pp. 237-288

[5] F. Marche Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects, Eur. J. Mech. B Fluids, Volume 26 (2007) no. 1, pp. 49-63

[6] J. Pedlowski Geophysical Fluid Dynamics, Springer-Verlag, New York, 1987

[7] R. Temam; M. Ziane Some mathematical problems in geophysical fluid dynamics, Handbook of Mathematical Fluid Dynamics, North-Holland, 2004

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