关于$\mathbb{R}^3$上不可压缩欧拉方程$C^{1， $ α}$解的自相似爆破的稳定性

IF 1.8 2区数学 Q1 MATHEMATICS

Cambridge Journal of Mathematics Pub Date : 2019-10-30 DOI:10.4310/cjm.2021.v9.n4.a4

T. Elgindi, T. Ghoul, N. Masmoudi

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引用次数: 20

摘要

我们研究了不可压缩欧拉方程最近构造的自相似爆破解的稳定性。我们工作的一个结果是有限能量$C^{1，\alpha}$解的存在性，这些解在有限时间内以局部自相似的方式变得奇异。作为推论，我们还观察到Beale Kato-Majda准则在$C^{1，\alpha}$解的类中不能改进。

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On the stability of self-similar blow-up for $C^{1,\alpha}$ solutions to the incompressible Euler equations on $\mathbb{R}^3$

We study the stability of recently constructed self-similar blow-up solutions to the incompressible Euler equation. A consequence of our work is the existence of finite-energy $C^{1,\alpha}$ solutions that become singular in finite time in a locally self-similar manner. As a corollary, we also observe that the Beale-Kato-Majda criterion cannot be improved in the class of $C^{1,\alpha}$ solutions.

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来源期刊

Cambridge Journal of Mathematics MATHEMATICS-

CiteScore

3.10

自引率

0.00%

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