ASYMPTOTIC STABILITY OF NONLINEAR WAVE FOR AN INFLOW PROBLEM TO THE COMPRESSIBLE NAVIER-STOKES-KORTEWEG SYSTEM

被引：0

作者：

Li, Yeping ^{[1
]}

Qian, Yujie ^{[1
]}

Yin, Rong ^{[1
]}

机构：

[1] Nantong Univ, Sch Math & Stat, Nantong 226019, Peoples R China

来源：

COMMUNICATIONS IN MATHEMATICAL SCIENCES | 2024年 / 22卷 / 06期

基金：

美国国家科学基金会;

关键词：

Compressible Navier-Stokes-Korteweg equation; Inflow problem; Rarefaction wave; Boundary layer solution; Asymptotic stability; Energy method; GLOBAL STRONG SOLUTION; FLUID MODELS; RAREFACTION WAVE; DIMENSIONAL SYSTEM; DECAY-RATE; EQUATIONS; EXISTENCE; CAPILLARITY; LIMIT;

D O I：

10.4310/CMS.2024.v22.n6.a3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we are concerned with the inflow problem on the half line (0 , + infinity) for a one-dimensional compressible Navier-Stokes-Korteweg system, which is used to model compressible viscous fluids with internal capillarity, i.e., the liquid-vap or mixtures with phase interfaces. We first investigate that the asymptotic profile is a nonlinear wave: the superposition wave of a rarefaction wave and a boundary layer solution under the proper condition of the far fields and boundary values. The asymptotic stability on the nonlinear wave is shown under some conditions that the initial data are a small perturbation of the rarefaction wave and the strength of the stationary wave is small enough. The proofs are given by an elementary energy method.

引用

页码：1501 / 1528

页数：28

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