Vacuum and singularity formation for compressible Euler equations with time-dependent damping

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/dcds.2022184

Ying Sui, Weiqiang Wang, Huimin Yu

引用次数: 1

Abstract

In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $ 1<\gamma{\leq} 3 $, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, we succeed in proving the singular formation theorem for all $ \lambda $, which was open in [19] for some cases. Moreover, the singularity formation of the compressible Euler equations when $ \gamma = 3 $ is investigated, too.

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具有时变阻尼的可压缩欧拉方程的真空和奇点形成

本文考虑了具有时变阻尼的可压缩欧拉方程的真空和奇点的形成。对于$ 1<\gamma{\leq} 3 $，通过巧妙地构造一些新的控制函数，我们得到了任意经典解的密度下界估计。基于这些较低的估计，我们成功地证明了所有$ \lambda $的奇异地层定理，该定理在[19]中对某些情况是开放的。此外，还研究了$ \gamma = 3 $时可压缩欧拉方程奇点的形成。

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

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

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