Asymptotic stability of rarefaction wave for the compressible Navier-Stokes-Korteweg equations in the half space

被引：9

作者：

Li, Yeping ^{[1
]}

Tang, Jing ^{[1
]}

Yu, Shengqi ^{[1
]}

机构：

[1] Nantong Univ, Sch Sci, Nantong 226019, Peoples R China

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2022年 / 152卷 / 03期

基金：

美国国家科学基金会;

关键词：

Compressible Navier-Stokes-Korteweg equation; Rarefaction wave; Asymptotic stability; Energy method; GLOBAL STRONG SOLUTION; OPTIMAL DECAY-RATES; LARGE-TIME BEHAVIOR; FLUID MODELS; INFLOW PROBLEM; DIMENSIONAL SYSTEM; CAPILLARITY LIMIT; BOUNDARY-LAYER; P-SYSTEM; EXISTENCE;

D O I：

10.1017/prm.2021.32

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, we are concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the Navier-Stokes Korteweg equations of a compressible fluid in the half space. We assume that the space-asymptotic states and the boundary data satisfy some conditions so that the time-asymptotic state of this solution is a rarefaction wave. Then we show that the rarefaction wave is non-linearly stable, as time goes to infinity, provided that the strength of the wave is weak and the initial perturbation is small. The proof is mainly based on L-2-energy method and some time-decay estimates in L-p-norm for the smoothed rarefaction wave.

引用

页码：756 / 779

页数：24

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