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February  2004, 10(1&2): 543-556. doi: 10.3934/dcds.2004.10.543

Regularity results for weak solutions of the 3D MHD equations

Jiahong Wu 1,

1. 

Department of Mathematics, Oklahoma State University, Stillwater, OK 74078, United States

Received  January 2002 Revised  May 2003 Published  October 2003

We study regularity of general and axisymmetric weak solutions of the 3D MHD equations with dissipation and resistance. A general weak solution is shown to be smooth if it satisfies a Serrin condition. The regularity of axisymmetric weak solutions is analyzed through the MHD equations in cylindrical coordinates, whose concrete form is derived here using Gibbs' notion of dyadic product. We establish that it is sufficient to impose conditions on certain components (in cylindrical coordinates) of an axisymmetric weak solution in order for the solution to be regular.
Keywords: weak solution, axisymmetry, MHD equations, global regularity..
Mathematics Subject Classification: 76W05, 76D03, 76DXX.
Citation: Jiahong Wu. Regularity results for weak solutions of the 3D MHD equations. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 543-556. doi: 10.3934/dcds.2004.10.543
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