Global well-posedness for the 2D micropolar Bénard convection system with mixed partial viscosity

Abstract

The micropolar Bénard system is derived from the convective motions in a heated and incompressible fluid. When there is only partial dissipation or no dissipation at all, the problem of whether the 2D micropolar Bénard convection system possesses a global classical solution is difficult to be solved. In this paper, we study the Cauchy problem of the two-dimensional micropolar Bénard problem with mixed partial viscosity. More precisely, the global regularity and some conditional regularity of strong solutions are obtained for 2D micropolar Bénard problem with mixed partial viscosity.