Global regularity of generalized MHD-Boussinesq equations
The purpose of this paper is to study the global well-posedness of generalized MHD-Boussinesq equations with only velocity dissipation in whole space Rn(n≥2).Firstly,by exploiting the structure of this system,we obtain the uniform L2-bound of the global solutions.Then,the uniform H1-bound of the global solutions is proved by making use of logarithmic type interpolation inequality and the improved Gronwall inequality.Finally,by using delicate energy estimates,we overcome the difficulty of lack of dissipation and establish the a priori uniform Hs(s＞1+n/2)estimate which proves the global existence and uniqueness of the classical solutions to this system.
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