可压缩 Navier-Stokes-Korteweg 系统流入问题非线性波的渐近稳定性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-18 DOI:10.4310/cms.2024.v22.n6.a3

Yeping Li, Yujie Qian, Rong Yin

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引用次数: 0

摘要

本文关注一维可压缩纳维-斯托克斯-科特韦格（Navier-Stokes-Korteweg）系统的半线$(0,+\infty)$上的流入问题，该系统用于模拟具有内毛细管性的可压缩粘性流体，即具有相界面的液气混合物。我们首先研究了渐近剖面是一种非线性波：在适当的远场和边界值条件下，稀释波和边界层解的叠加波。在初始数据是稀释波的小扰动和静止波强度足够小的条件下，非线性波的渐近稳定性得到了证明。证明采用基本能量法。

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Asymptotic stability of nonlinear wave for an inflow problem to the compressible Navier-Stokes-Korteweg system

In this paper, we are concerned with the inflow problem on the half line $(0,+\infty)$ for a one-dimensional compressible Navier-Stokes-Korteweg system, which is used to model compressible viscous fluids with internal capillarity, i.e., the liquid-vapor 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.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.