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Prandtl Boundary Layer and Complex Fluids

讲座摘要

In this talk we 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 boundary layer solutions and the justification of Prandtl boundary layer ansatz 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 Prandtl boundary layer theory in complex fluids, such as Magneto-hydrodynamics. The solvability of MHD boundary layer equations and the validity of Prandtl boundary layer ansatz for MHD equations in Sobolev spaces are addressed for two different cases: the tangential magnetic field dominates; the normal magnetic field dominates.



报告人简介
谢峰,上海交通大学教授、德国洪堡学者。近年来主要研究流体力学中的非线性偏微分方程解的多尺度分析和奇异极限等。特别是,Prandtl 流体边界层的稳定性和高雷诺数极限的数学理论。部分研究成果发表在 CPAM, JFA, SIMA,JDE 等本领域有影响力的学术期刊上。曾受邀作第八届华人数学家大会一小时报告,担任 SCI 杂志 CPAA 编委。