Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity

Abstract

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We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The\ndiffusion of mixed partial viscosity is weaker than that of full viscosity, which cases\nnew difficulty in proving global smooth solutions. Moreover, Hall term heightens the\nlevel of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the\ninitial data is enough small.<\/p>"