The article is devoted to the study of Cauchy problem to the Rayleigh–Bénard convection model for the micropolar fluid in two dimensions. We first prove the unique local solvability of smooth solution to the system when the system has only velocity dissipation, and then establish a criterion for the breakdown of smooth solutions imposed only the maximum norm of the gradient of scalar temperature field. Finally, we show the global regularity of the system with zero angular viscosity.

中文翻译：

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关于二维微极瑞利-贝纳德对流问题的适定性

本文专门针对二维微极性流体的Rayleigh-Bénard对流模型的Cauchy问题进行研究。当系统仅具有速度耗散时，我们首先证明了系统对光滑解的唯一局部可解性，然后建立了仅对标量温度场梯度的最大范数强加对光滑解的破坏的判据。最后，我们展示了零角粘度时系统的整体规律。