报告人：刘成杰 研究员（上海交通大学）

报告题目：Prandtl boundary layer theory for MHD equations in Sobolev spaces without monotonicity

报告摘要：In this talk, we study the validity of the Prandtl boundary layer theory for MHD equations in the half plane with no-slip boundary conditions on the velocity vector and the perfect conducting boundary conditions on the magnetic field. In the case that viscosity and magnetic diffusion tend to zero at the same rate, we derive the Prandtl-type boundary layer problem and establish the well-posedness result in Sobolev spaces under the assumption of nonzero initial tangential magnetic field, without any monotonicity assumption on the velocity, which is different from the classical Prandtl equation. Then, when the initial tangential magnetic field of MHD doesn't vanish at the boundary, we justify the validity of corresponding Prandtl boundary layer expansions in the Sobolev framework. This justifies the physical understanding that the magnetic field has a stabilizing effect on MHD boundary layer in rigorous mathematics. This is a joint work with Prof. Feng Xie and Prof.Tong Yang.

报告人简介：刘成杰博士于2014年于上海交通大学数学系获博士学位。2014至2017年在香港城市大学从事博士后工作，期间曾至香港中文大学任助理研究员。2017年9月进入上海交通大学自然科学研究院/数学科学学院工作。刘成杰近几年一直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，尤其是在三维Prandtl方程组的适定性理论和磁流体边界层的稳定性理论方面等。这些结果发表Comm. Pure Appl. Math.，Adv. Math.，Arch. Ration. Mech. Anal., J. Math. Pures Appl., SIAM J. Math. Anal. 等偏微分领域具有重要影响力的期刊上。

报告时间：2019年6月16日（星期日）下午16:00

报告地点：科技楼南楼702