Abstract:

       We study how an impressed magnetic field can influence the time-asymptotic behavior of strong solutions of 2D incompressible non-resistive viscous magnetohydrodynamic (MHD) fluids with large initial perturbation in Lagrangian coordinates. We show the existence of a unique strong solution with some class of large initial perturbation, where the largeness of the initial data depends on the strength of the impressed magnetic field. Moreover, we deduce the time-decay rates of the strong solution, and establish a convergence result with convergence rates of the strong solution to the solution of the linearized problem as the strength of the impressed magnetic field goes to infinity. In addition, similar results can be also extended to the corresponding inviscid MHD system with damping. Finally, for this inviscid MHD system with damping, we show that a strong horizontal impressed magnetic field still can inhibit the Rayleigh-Taylor instability. (joint-work with Fei Jiang)

嘉宾简介：

       江松， 应用数学家，北京应用物理与计算数学研究所研究员。1982年毕业于四川大学数学系，1984年在西安交通大学获硕士学位，1988年在德国波恩大学获博士学位。2015年当选中国科学院院士。

       主要从事可压缩流体力学数学理论、计算方法及应用研究。在理论方面，对任何绝热指数γ>1，与合作者证明了具有大外力的三维定常可压缩Navier-Stokes (NS)方程弱解的存在性，以及具有大初值的高维非定常NS方程球/轴对称解的整体存在性。在应用方面，针对武器物理数值模拟的多介质大变形、网格畸变等计算难点，与同事一起提出了若干实用的新算法（如整体ALE局部欧拉自然耦合方法），并研制完成重大武器型号数值模拟软件平台。曾获国家自然科学二等奖、军队科技进步一等奖、中国青年科技奖、求是杰出青年奖等。