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.

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