Compressible primitive equations: formal derivation and stability of weak solutions

被引：22

作者：

Ersoy, Mehmet ^{[1
,3
]}

Ngom, Timack ^{[1
,2
]}

Sy, Mamadou ^{[2
]}

机构：

[1] Univ Savoie, CNRS, LAMA, UMR 5127, F-73376 Le Bourget Du Lac, France

[2] Univ Gaston Berger St Louis, UFR SAT, LANI, St Louis, Senegal

[3] BCAM, Derio 48160, Basque Country, Spain

来源：

NONLINEARITY | 2011年 / 24卷 / 01期

关键词：

NAVIER-STOKES EQUATIONS; ATMOSPHERE;

D O I：

10.1088/0951-7715/24/1/004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a formal derivation of compressible primitive equations for atmosphere modelling. They are obtained from the 3D compressible Navier-Stokes equations with an anisotropic viscous stress tensor depending on the density. Then, we study the stability of weak solutions to this problem by introducing an intermediate model obtained by a suitable change of variables. This intermediate model is more practical and it is simpler to achieve the main result.

引用

页码：79 / 96

页数：18

共 13 条

[1]

[Anonymous], 2004, SOME MATH PROBLEMS G

[2] Some diffusive capillary models of Korteweg type [J].

Bresch, D ;

Desjardins, B .

COMPTES RENDUS MECANIQUE, 2004, 332 (11) :881-886

[3] Global Weak Solutions to a Generic Two-Fluid Model [J].

Bresch, D. ;

Desjardins, B. ;

Ghidaglia, J. -M. ;

Grenier, E. .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2010, 196 (02) :599-629

[4] On compressible Navier-Stokes equations with density dependent viscosities in bounded domains [J].

Bresch, Didier ;

Desjardins, Benoit ;

Gerard-Varet, David .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 87 (02) :227-235

[5]

Bresch D, 2009, HBK DIFF EQUAT EVOL, V5, P1, DOI 10.1016/S1874-5717(08)00208-9

[6]

BUNTEBARTH G, 1981, ABHUNDLUNGEN BRAUNSC, V32, P95

[7]

ERSOY M, 2010, EXISTENCE GLOBAL WEA

[8] Existence of a global solution to one model problem of atmosphere dynamics [J].

Gatapov, BV ;

Kazhikhov, AV .

SIBERIAN MATHEMATICAL JOURNAL, 2005, 46 (05) :805-812

[9]

Kochin N.E., 1936, T GLAVN GEOFIZ OBS, V4, P21

[10] NEW FORMULATIONS OF THE PRIMITIVE EQUATIONS OF ATMOSPHERE AND APPLICATIONS [J].

LIONS, JL ;

TEMAM, R ;

WANG, SH .

NONLINEARITY, 1992, 5 (02) :237-288

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