Existence Of Global Solutions To A Class Of Two-dimensional MHD-Boussinesq Equations

Magnetic fluid mechanics(Magnetohydrodynamics,MHD)equations describe the interaction between magnetic field and conductive fluid.Boussinesq equations are a class of nonlinear equations describing atmospheric motion.Existence of global strong solutions for initial value problems MHD-Boussinesq coupled equations is studied.The existence of unique solutions in Hs(R2)of approximate equations is first proved;Then by approximating the prior estimation of the solution of the equations and the compactness theorem of space,Prove the initial data(u0,b0,?0)? Hs(R2),s>2 and ?·u0=?·b0=0,the initial value problem of MHD-Boussinesq equations,there are local solutions and global solutions.