三维广义MHD方程和Boussinesq方程正则性准则的注记

Abstract

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

CLC Number:

O175.2

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

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