Global Well-posedness for the 2D Micropolar Rayleigh–Bénard Convection Problem without Velocity Dissipation

In this article, we study the Cauchy problem to the micropolar Rayleigh–Bénard 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.