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Weak Serrin-type blow-up criterion and global strong solution of nonhomogeneous incompressible micropolar fluid equations with vacuum

主讲人：李焕元

摘要：This talk is concerned with a Cauchy problem for the three-dimensional (3D) nonhomogeneous incompressible micropolar fluid equations  in the whole space. We first establish a weak Serrin-type blowup criterion for the strong solutions. It is shown that for the Cauchy problem of the 3D nonhomogeneous micropolar equations, the strong solution exists globally if the velocity satisfies the weak Serrin's condition. In particular, this criterion is independent of the micro-rotational velocity. Then as an immediate application, we prove that the Cauchy problem of micropolar fluid equations has a unique global strong solution, provided that the kinematic viscosity is sufficiently large, or the upper bound of initial density or initial kinetic energy is small enough.

主讲人简介：刘双乾，华中师范大学数学与统计学院教授，2009年博士毕业于武汉大学，主要研究方向为动理学方程的数学理论，对低正则函数空间和临界Besov空间中Boltzmann方程及相关复杂动理学模型的整体适定性、初边值问题的整体可解性、流体动力学极限等问题取得了一系列重要成果，在Commun. Pure Appl. Math.、Commun. Math. Phys.、Arch. Ration. Mech. Anal.、 Trans. Amer. Math. Soc.、J. Funct. Anal.、SIAM J. Math. Anal.等国际主流数学杂志发表论文数十篇。

邀请人：雷远杰

时间：：2022年7月13日 （星期三）14: 30-16:00  

地点：腾讯会议室     ID:736 682 488