Improved regularity criteria for the MHD equations

IF 1.2 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Journal of Mathematical Physics Pub Date : 2024-08-01 DOI:10.1063/5.0179393

Weihua Wang, Shixia Xu

引用次数: 0

Abstract

In this paper, we establish new regularity criteria for the three-dimensional (3D) viscous incompressible magnetohydrodynamic (MHD) equations. It is proved that if the solution of the MHD equations satisfies u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞, then the regularity of the solution on (0, T), where u3, j3 and ω3 are the third component of velocity u, current density ∇ × b and vorticity ∇ × u, respectively. These results give new improvements of regularity theory of weak solutions.

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改进的多流体力学方程正则准则

本文为三维（3D）粘性不可压缩磁流体动力学（MHD）方程建立了新的正则性准则。研究证明，如果 MHD 方程的解满足 u3∈Lp(0,T;Lq(R3)),j3∈Lr(0,T；Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞ or u3∈Lp(0,T;Lq(R3)),w3∈Lr(0,T;Ls(R3)),2p+3q=1324,7213≤q≤∞;2r+3s=2,32<s≤∞，那么解在（0，T）上的正则性，其中 u3、j3 和 ω3 分别是速度 u、电流密度 ∇ × b 和涡度 ∇ × u 的第三分量。这些结果对弱解的正则性理论有了新的改进。

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

Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

2.20

自引率

15.40%

发文量

396

审稿时长

4.3 months

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