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

Abstract

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small. AMS Subject Classifications: 76D03, 76W05 Chinese Library Classifications: O175.29