On the interior regularity conditions of a suitable weak solution to 3D MHD equations

被引:0
作者
Kim, Jae-Myoung [1 ]
机构
[1] Andong Natl Univ, Dept Math Educ, Andong 36729, South Korea
来源
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2024年 / 31卷 / 06期
基金
新加坡国家研究基金会;
关键词
Suitable weak solution; Local regularity condition; 3D MHD equations;
D O I
10.1007/s00030-024-01002-w
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study the local interior regularity condition of a suitable weak solution to MHD equations. We prove that if a vorticity, w belong to Lx,tp,q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{x,t}<^>{p,q}$$\end{document} in a neighborhood of an interior point with 3p+2q <= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{3}{p} + \frac{2}{q} \le 2$$\end{document} and 32<p<infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{3}{2}< p < \infty $$\end{document}, then solution is regular near that point. Also, we show the result of the component reduction in this direction.
引用
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页数:11
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