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

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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.