The Well Posedness for Nonhomogeneous Boussinesq Equations

This paper is devoted to studying the Cauchy problem for non-homogeneous Boussinesq equations. We built the results on the critical Besov spaces (?,u)& ISIN;LT infinity(Bp,1N/p)xLT infinity(Bp,1N/p-1)?LT1(Bp,1N/p+1) with 1 p < 2N. We proved the global existence of the solution when the initial velocity is small withrespect to the viscosity, as well as the initial temperature approaches a positive constant. Furthermore, weproved the uniqueness for1 < p=N. Our results can been seen as a version of symmetry in Besov spacefor the Boussinesq equations.