三维广义MHD方程和Boussinesq方程正则性准则的注记

摘要/Abstract

摘要：

该文研究三维具有分数阶耗散项的广义MHD方程，得到了在负指标齐次Besov空间意义下速度场u与磁场b和的正则性准则，推广了已有结论.另外，该文还得到了三维分数阶耗散广义Boussinesq方程光滑解关于速度梯度的一个正则性准则.

关键词: 广义MHD方程, 广义Boussinesq方程, 正则性准则, Besov空间

Abstract:

In this paper, we study the 3D generalized MHD system with dissipation and diffusion in terms of fractional Laplacian. We obtain a regularity criterion of solution for the generalized MHD equations in terms of the summation of velocity field u and magnetic field b under the framework of homogeneous Besov space with negative indices, which extends the previous results. We also present a regularity criterion of smooth solution to the 3D generalized Boussinesq equations with fractional dissipation in terms of the gradient of velocity only.

Key words: Generalized MHD equations, Generalized Boussinesq equations, Regularity criterion, Besov spaces

中图分类号:

O175.2

邱华,谢常平,房少梅. 三维广义MHD方程和Boussinesq方程正则性准则的注记[J]. 数学物理学报, 2019, 39(2): 316-328.

Hua Qiu,Changping Xie,Shaomei Fang. Remarks on Regularity Criteria for 3D Generalized MHD Equations and Boussinesq Equations[J]. Acta mathematica scientia,Series A, 2019, 39(2): 316-328.

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