Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space

被引：72

作者：

Kagei, Yoshiyuki ^{[1
]}

Kawashima, Shuichi ^{[1
]}

机构：

[1] Kyushu Univ, Fac Math, Fukuoka 8128581, Japan

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2006年 / 266卷 / 02期

关键词：

Half Space; Weak Sense; Local Existence; Stokes System; Decay Property;

D O I：

10.1007/s00220-006-0017-1

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Stability of planar stationary solutions to the compressible Navier-Stokes equation on the half space R-+(n)(n >= 2) under outflow boundary condition is investigated. It is shown that the planar stationary solution is stable with respect to small perturbations in H-s (R-+(n)) with s >= [n/2] + 1 and the perturbations decay in L-infinity norm as t --> infinity, provided that the magnitude of the stationary solution is sufficiently small. The stability result is proved by the energy method. In the proof an energy functional based on the total energy of the system plays an important role.

引用

页码：401 / 430

页数：30

共 7 条

[1]

Friedman A., 1969, PARTIAL DIFFERENTIAL

[2]

Galdi G.P., 1994, INTRO MATH THEORY NA, VI

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