Asymptotic Behavior of Solutions to the Compressible Navier-Stokes Equation Around a Parallel Flow

被引：27

作者：

Kagei, Yoshiyuki ^{[1
]}

机构：

[1] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2012年 / 205卷 / 02期

关键词：

LARGE-TIME BEHAVIOR; INFINITE-LAYER; HALF-SPACE;

D O I：

10.1007/s00205-012-0516-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The initial boundary value problem for the compressible Navier-Stokes equation is considered in an infinite layer of . It is proved that if the Reynolds and Mach numbers are sufficiently small, then strong solutions to the compressible Navier-Stokes equation around parallel flows exist globally in time for sufficiently small initial perturbations. The large time behavior of the solution is described by a solution of a one-dimensional viscous Burgers equation. The proof is given by a combination of spectral analysis of the linearized operator and a variant of the Matsumura-Nishida energy method.

引用

页码：585 / 650

页数：66

共 16 条

[1]

[Anonymous], 1994, An introduction to the mathematical theory of the Navier-Stokes equations

[2]

[Anonymous], 2010, J MATH FOR IND A, V2A, P39

[3] TRANSPORT AND PROPAGATION OF A PERTURBATION OF A FLOW OF A COMPRESSIBLE FLUID IN A BOUNDED REGION [J].

GEYMONAT, G ;

LEYLAND, P .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1987, 100 (01) :53-81

[4]

Iooss G., 1998, ANN U FERRARA, V43, P157

[5] Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system [J].

Kagei, Y ;

Kawashima, S .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2006, 3 (02) :195-232

[6] Asymptotic behavior of solutions of the compressible Navier-Stokes equations on the half space [J].

Kagei, Y ;

Kobayashi, T .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2005, 177 (02) :231-330

[7]

Kagei Y., 2010, J MATH FOR IND B, V2B, P235

[8] Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer [J].

Kagei, Yoshiyuki .

HIROSHIMA MATHEMATICAL JOURNAL, 2008, 38 (01) :95-124

[9] Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer [J].

Kagei, Yoshiyuki .

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2007, 43 (03) :763-794

[10] Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space [J].

Kagei, Yoshiyuki ;

Kawashima, Shuichi .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 266 (02) :401-430

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