改进的多流体力学方程正则准则

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

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引用次数: 0

摘要

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。

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Improved regularity criteria for the MHD equations

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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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

期刊介绍： Since 1960, the Journal of Mathematical Physics (JMP) has published some of the best papers from outstanding mathematicians and physicists. JMP was the first journal in the field of mathematical physics and publishes research that connects the application of mathematics to problems in physics, as well as illustrates the development of mathematical methods for such applications and for the formulation of physical theories. The Journal of Mathematical Physics (JMP) features content in all areas of mathematical physics. Specifically, the articles focus on areas of research that illustrate the application of mathematics to problems in physics, the development of mathematical methods for such applications, and for the formulation of physical theories. The mathematics featured in the articles are written so that theoretical physicists can understand them. JMP also publishes review articles on mathematical subjects relevant to physics as well as special issues that combine manuscripts on a topic of current interest to the mathematical physics community. JMP welcomes original research of the highest quality in all active areas of mathematical physics, including the following: Partial Differential Equations Representation Theory and Algebraic Methods Many Body and Condensed Matter Physics Quantum Mechanics - General and Nonrelativistic Quantum Information and Computation Relativistic Quantum Mechanics, Quantum Field Theory, Quantum Gravity, and String Theory General Relativity and Gravitation Dynamical Systems Classical Mechanics and Classical Fields Fluids Statistical Physics Methods of Mathematical Physics.