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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:
35Q35PDEs in connection with fluid mechanics
35Q30Stokes and Navier-Stokes equations
35B65Smoothness and regularity of solutions of PDE