GLOBAL WELL-POSEDNESS FOR N-DIMENSIONAL BOUSSINESQ SYSTEM WITH VISCOSITY DEPENDING ON TEMPERATURE

In this paper, we study the global well-posedness issue for the Boussinesq system with the temperature-dependent viscosity in R-n (n >= 2). With a temperature damping term, we first get a global solution in R-2, provided the initial temperature is exponentially small compared with the initial velocity field. Then, using a weighted Chemin-Lerner-type norm, we can also give a global large solution in R n if the initial data satisfies a nonlinear smallness condition. In particular, our results imply the global large solutions without any smallness conditions imposed on the initial velocity.