三维广义MHD方程和Boussinesq方程正则性准则的注记

数学物理学报 ›› 2019, Vol. 39 ›› Issue (2): 316-328.

三维广义MHD方程和Boussinesq方程正则性准则的注记

邱华¹,谢常平²,房少梅^3,*()

^{1, 2, 3} 华南农业大学数学与信息学院广州 510642
³ 长江师范学院数学与统计学院重庆 408100

收稿日期:2018-01-12 出版日期:2019-04-26 发布日期:2019-05-05
通讯作者: 房少梅 E-mail:dz90@scau.edu.cn
基金资助:
国家自然科学基金(11126266);国家自然科学基金(11271141);广东省自然科学基金( );家留学基金委员会

Remarks on Regularity Criteria for 3D Generalized MHD Equations and Boussinesq Equations

Hua Qiu¹,Changping Xie²,Shaomei Fang^3,*()

^{1, 2, 3} College of Mathematics and Informatics, South China Agricultural University, Guangzhou 510642
³ School of Mathematics and Statistics, Yangtze Normal University, Chongqing 408100

Received:2018-01-12 Online:2019-04-26 Published:2019-05-05
Contact: Shaomei Fang E-mail:dz90@scau.edu.cn
Supported by:
the NSFC(11126266);the NSFC(11271141);the Natural Science Foundation of Guangdong Province( );the China Scholarship Council

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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