Global well-posedness for the 2D micropolar Rayleigh-B\'{e}nard convection problem

In this article, we study the Cauchy problem to the micropolar Rayleigh-B'{e}nard convection problem without velocity dissipation in two dimension. We first prove the local well-posedness of a smooth solution, and then establish a blow up criterion in terms of the gradient of scalar temperature field. At last, we obtain the global well-posedness to the system.