On global solutions of Cauchy problems for compressible Navier-Stokes equations

被引：16

作者：

Kawashita, M ^{[1
]}

机构：

[1] Ibaraki Univ, Fac Educ, Mito, Ibaraki 3108512, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2002年 / 48卷 / 08期

关键词：

compressible fluid flows; compressible Navier-Stokes equations; Cauchy problems; initial problems; strong solutions; global solutions;

D O I：

10.1016/S0362-546X(00)00238-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The existence and uniqueness of solutions of the compressible Navier-Stokes equation were analyzed. The uniqueness and global existence of solutions were demonstrated for compressible viscous and heat conductive fluids. When the viscosity coefficients depended on density and the fluid stayed in an exterior domain. The asymptotic behavior of the solutions was analyzed. The decay rate of the solution with small initial data was derived for Cauchy problem.

引用

收藏

页码：1087 / 1105

页数：19

相关论文

共 11 条

[1] L(2) DECAY FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN UNBOUNDED-DOMAINS [J].

DECKELNICK, K .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1993, 18 (9-10) :1445-1476

[2] STRONG-CONVERGENCE TO GLOBAL-SOLUTIONS FOR MULTIDIMENSIONAL FLOWS OF COMPRESSIBLE, VISCOUS FLUIDS WITH POLYTROPIC EQUATIONS OF STATE AND DISCONTINUOUS INITIAL DATA [J].

HOFF, D .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1995, 132 (01) :1-14

[3] MULTIDIMENSIONAL DIFFUSION WAVES FOR THE NAVIER-STOKES EQUATIONS OF COMPRESSIBLE FLOW [J].

HOFF, D ;

ZUMBRUN, K .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1995, 44 (02) :603-676

[4] GLOBAL-SOLUTIONS OF THE NAVIER-STOKES EQUATIONS FOR MULTIDIMENSIONAL COMPRESSIBLE FLOW WITH DISCONTINUOUS INITIAL DATA [J].

HOFF, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1995, 120 (01) :215-254

[5] EXTENDED KORN INEQUALITIES AND THE ASSOCIATED BEST POSSIBLE CONSTANTS [J].

ITO, H .

JOURNAL OF ELASTICITY, 1990, 24 (1-3) :43-78

[6] Decay estimates of solutions for the equations of motion of compressible viscous and heat-conductive gases in an exterior domain in R3 [J].

Kobayashi, T ;

Shibata, Y .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1999, 200 (03) :621-659

[7] INITIAL BOUNDARY-VALUE-PROBLEMS FOR THE EQUATIONS OF MOTION OF COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE FLUIDS [J].

MATSUMURA, A ;

NISHIDA, T .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 89 (04) :445-464

[8] INITIAL VALUE-PROBLEM FOR THE EQUATIONS OF MOTION OF COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE FLUIDS [J].

MATSUMURA, A ;

NISHIDA, T .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1979, 55 (09) :337-342

[9]

Matsumura A., 1980, J. Math. Kyoto Univ., V20, P67

[10] GLOBAL EXISTENCE OF SMALL SOLUTIONS TO A CLASS OF NONLINEAR EVOLUTION-EQUATIONS [J].

PONCE, G .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1985, 9 (05) :399-418