Remarks on the smoothness of the C1,α asymptotically self-similar singularity in the 3D Euler and 2D Boussinesq equations

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-05-13 DOI:10.1088/1361-6544/ad45a2

Jiajie Chen

引用次数: 0

Abstract

We show that the constructions of asymptotically self-similar singularities for the three-dimensional (3D) Euler equations by Elgindi, and for the 3D Euler equations with large swirl and 2D Boussinesq equations with boundary by Chen-Hou can be extended to construct singularity with velocity that is not smooth at only one point. The proof is based on a carefully designed small initial perturbation to the blowup profile, and a BKM-type continuation criterion for the one-point nonsmoothness. We establish the criterion using weighted Hölder estimates with weights vanishing near the singular point. Our results are inspired by the recent work of Cordoba, Martinez-Zoroa and Zheng that it is possible to construct a singularity for the 3D axisymmetric Euler equations without swirl and with velocity .

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关于三维欧拉方程和二维布辛斯方程中 C1,α 渐近自相似奇点平滑性的评论

我们证明，Elgindi 对三维（3D）欧拉方程的渐近自相似奇点构造，以及 Chen-Hou 对有大漩涡的三维欧拉方程和有边界的二维布森斯克方程的奇点构造，可以扩展到构造速度仅在一点不光滑的奇点。证明基于对吹胀轮廓精心设计的小初始扰动，以及单点非光滑性的 BKM 型延续准则。我们利用在奇异点附近权重消失的加权赫尔德估计建立了该准则。我们的研究结果受到了 Cordoba、Martinez-Zoroa 和 Zheng 最近研究的启发，即有可能为无漩涡和速度为...的三维轴对称欧拉方程构建奇点。

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

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.