数学与统计学院学术报告[2020] 142号

(高水平大学建设系列报告495号)

报告题目: MHD boundary layer and Vanishing viscosity limit

报告人： 谢峰 教授  （上海交通大学）

报告时间：2020年 12月10日 15：00-15：45

报告地点： 腾讯会议 406 643 573 　

报告内容： In this talk I will recall the classical Prandtl boundary layer double-scale asymptotical expansions in the analysis of structure of fluids with the high Reynolds number in a domain with boundaries. Vanishing viscosity limit can be regarded as a direct application of Prandtl boundary layer asymptotical expansions.  The Prandtl boundary layer theory includes the well-posedness of solutions to the Prandtl boundary layer equations and the justification of Prandtl boundary layer asymptotical expansions etc. Motivated by one open problem in the classical book “Mathematical models in Boundary Layer Theory” by O.A. Oleinik and V.N. Samokhin. We consider the boundary layer theory in Magneto Hydrodynamics. The solvability of MHD boundary layer equations and the validity of Prandtl boundary layer ansatz for MHD equations are studied in Sobolev spaces. Compared with the well-posedness theory of the classical Prandtl equations for which the monotonicity condition of the tangential velocity plays a crucial role, this monotonicity condition is not needed for MHD boundary layer any more. Moreover, the validity of Prandtl boundary layer ansatz for MHD is also achieved in Sobolev spaces.

报告人简历：谢峰教授主要从事非线性偏微分方程和流体力学边界层及相关问题的数学理论的研究，在流体边界层的数学理论方面取得了一系列的研究成果，尤其是在磁流体边界层的稳定性和高雷诺数极限等方面的研究。这些结果发表Comm. Pure Appl. Math.，JFA， SIAM J. Math. Anal. 等偏微分领域具有重要影响力的期刊上。

欢迎感兴趣的师生参加！

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                                                2020年12月09日