ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

被引：12

作者：

Hong, Hakho ^{[1
]}

Huang, Feimin ^{[2
]}

机构：

[1] Acad Sci, Inst Math, Pyonyang, North Korea

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2012年 / 32卷 / 01期

关键词：

compressible Navier-Stokes equations; free boundary; superposition of shock wave and contact discontinuity; stability; NONLINEAR STABILITY; RAREFACTION WAVES; GLOBAL STABILITY; SYSTEM; GAS;

D O I：

10.1016/S0252-9602(12)60025-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

引用

页码：389 / 412

页数：24

共 22 条

[1] SIMILARITY SOLUTIONS OF NONLINEAR DIFFUSION EQUATION [J].