Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system of equations

被引：131

作者：

Mellet, A. ^{[1
]}

Vasseur, A. ^{[2
]}

机构：

[1] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2007年 / 17卷 / 07期

基金：

美国国家科学基金会;

关键词：

Vlasov equations; compressible Navier-Stokes equations; fluid-particles models; existence analysis;

D O I：

10.1142/S0218202507002194

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the existence of a weak solutions for a coupled system of kinetic and fluid equations. More precisely, we consider a Vlasov-Fokker-Planck equation coupled to compressible Navier-Stokes equation via a drag force. The fluid is assumed to be barotropic with gamma-pressure law (gamma > 3/2). The existence of weak solutions is proved in a bounded domain of R-3 with homogeneous Dirichlet conditions on the fluid velocity field and Dirichlet or reflection boundary conditions on the kinetic distribution function.

引用

页码：1039 / 1063

页数：25

共 26 条

[1]

BARANGER C, 2006, IN PRESS J DIFF HYPE

[2] Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression [J].

Berres, S ;

Bürger, R ;

Karlsen, KH ;

Tory, EM .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 64 (01) :41-80

[3] From kinetic equations to multidimensional isentropic gas dynamics before shocks [J].

Berthelin, F ;

Vasseur, A .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (06) :1807-1835

[4] Asymptotic behavior of an initial-boundary value problem for the Vlasov-Poisson-Fokker-Planck system [J].

Bonilla, LL ;

Carrillo, JA ;

Soler, J .

SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (05) :1343-1372

[5] EXISTENCE AND UNIQUENESS OF A GLOBAL SMOOTH SOLUTION FOR THE VLASOV-POISSON-FOKKER-PLANCK SYSTEM IN 3 DIMENSIONS [J].

BOUCHUT, F .

JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 111 (01) :239-258

[6]

Carrillo JA, 1998, MATH METHOD APPL SCI, V21, P907, DOI 10.1002/(SICI)1099-1476(19980710)21:10<907::AID-MMA977>3.3.CO

[7]

2-N

[8] Stability and asymptotic analysis of a fluid-particle interaction model [J].

Carrillo, Jose A. ;

Goudon, Thierry .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2006, 31 (09) :1349-1379

[9]

Cercignani C., 1994, MATH THEORY DILUTE G, V106

[10]

DAFERMOS CM, 1979, ARCH RATION MECH AN, V70, P167, DOI 10.1007/BF00250353

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