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.

中文翻译：

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无速度耗散的二维微极瑞利-贝纳对流问题的全局适定性

在本文中，我们研究了二维无速度耗散的微极 Rayleigh-Bénard 对流问题的柯西问题。我们首先证明了光滑解的局部适定性，然后根据标量温度场的梯度建立了一个爆破判据。最后，我们获得了系统的全局适定性。