A review of recent applications of the relative entropy method to discontinuous solutions of conservation laws

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-04-26 DOI:10.1090/qam/1667

A. Vasseur

引用次数: 0

Abstract

Dafermos [Arch. Rational Mech. Anal. 70 (1979), pp. 167–179] proved the weak/strong principle for conservation laws. It states that Lipschitz solutions to conservation laws endowed with convex entropies are unique and stable among weak solutions. The method, based on relative entropy, was extended by Di Perna [Indiana Univ. Math. J. 28 (1979), pp. 137–188] to show the uniqueness of shocks among weak solutions with strong traces. This theory has been recently revisited with the notion of weighted contractions up to shifts. We review in this paper recent applications of this method, including the weak/BV principle and the stability of discontinuous solutions among inviscid double limits of Navier-Stokes systems.

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相对熵法在守恒律不连续解中的最新应用综述

Dafermos[拱。合理的机械。[论文集，70(1979)，第167-179页]证明了守恒定律的弱/强原理。说明了具有凸熵的守恒律的Lipschitz解在弱解中是唯一且稳定的。这种基于相对熵的方法，由印第安纳大学数学学院的Di Perna进行了扩展。J. 28 (1979)， pp. 137-188]，以显示具有强迹的弱解中激波的唯一性。这个理论最近被重新审视，提出了加权收缩到位移的概念。本文综述了该方法的最新应用，包括弱/BV原理和Navier-Stokes系统无粘双极限间不连续解的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.