Global existence and uniqueness for a non linear Boussinesq system in dimension two

Abstract

We study the global well-posedness of a two-dimensional Boussinesq system which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion of type $|\DD|^α$ for the temperature. We prove that for $\alpha >1,$ there exists a unique global solution for initial data with critical regularities.

28 pages; Journal of Mathematics Physics, volume 51, no. 9 (2010)