Uniqueness of Composite Wave of Shock and Rarefaction in the Inviscid Limit of Navier–Stokes Equations

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-06-04 DOI:10.1137/23m156584x

Feimin Huang, Weiqiang Wang, Yi Wang, Yong Wang

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引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3924-3967, June 2024.
Abstract. The uniqueness of entropy solution for the compressible Euler equations is a fundamental and challenging problem. In this paper, the uniqueness of a composite wave of shock and rarefaction of one-dimensional compressible Euler equations is proved in the inviscid limit of compressible Navier–Stokes equations. Moreover, the relative entropy around the original Riemann solution consisting of shock and rarefaction under the large perturbation is shown to be uniformly bounded by the framework developed in [M. J. Kang and A. F. Vasseur, Invent. Math., 224 (2021), pp. 55–146]. The proof contains two new ingredients: (1) a cut-off technique and the expanding property of rarefaction are used to overcome the errors generated by the viscosity related to inviscid rarefaction; (2) the error terms concerning the interactions between shock and rarefaction are controlled by the compressibility of shock, the decay of derivative of rarefaction, and the separation of shock and rarefaction as time increases.

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纳维-斯托克斯方程不粘性极限中冲击和稀释复合波的唯一性

SIAM 数学分析期刊》，第 56 卷第 3 期，第 3924-3967 页，2024 年 6 月。摘要。可压缩欧拉方程熵解的唯一性是一个基本问题，也是一个具有挑战性的问题。本文在可压缩 Navier-Stokes 方程的不粘性极限中证明了一维可压缩欧拉方程的冲击波和稀释波复合解的唯一性。此外，通过[M. J. Kang and A. F. Vasseur, Invent. Math., 224 (2021), pp.］证明包含两个新要素：(1) 使用截止技术和稀释的膨胀特性来克服与无粘性稀释有关的粘度所产生的误差；(2) 有关冲击和稀释之间相互作用的误差项受冲击的可压缩性、稀释导数的衰减以及随着时间的增加冲击和稀释的分离所控制。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.