有速度排列的可压缩欧拉系统稀释波的渐近稳定性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-06 DOI:10.1088/1361-6544/ad422b

Xiang Bai, Lin-An Li and Xiaojing Xu

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引用次数: 0

摘要

本文研究了具有非局部速度排列的一维可压缩欧拉系统的稀释波渐近稳定性。也就是说，对于接近稀释波的初始数据，我们证明了相应的解向稀释波收敛。此外，我们还得到了该系统的弱对齐行为。我们通过傅立叶分析工具，对平滑近似稀释波进行了一些推广估计和新的先验估计。此外，我们还引入了加权能量法和贝索夫空间来获得关键的高阶导数估计，从而克服了非局部速度配准所带来的困难。值得一提的是，这是第一个针对速度对齐的可压缩欧拉系统的稀释波稳定性结果。

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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Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment

In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.