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Regularity criteria for the generalized viscous MHD equations. (English) Zbl 1130.35110
Generalized 3D viscous MHD equations are considered. Navier-Stokes and standard MHD equations are obtained for particular values of parameters. A regularity criteria, similar to Serrin’s regularity class for Navier-Stokes equations is given, and a smooth solution on $(0,T]$ interval is obtained. A weak solution is considered, which becomes strong if the corresponding vorticity field belongs to a particular Hölder space. The main tools are interpolation and inequalities in fractional Sobolev spaces.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 35Q30 Stokes and Navier-Stokes equations 35B65 Smoothness and regularity of solutions of PDE
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##### References:
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