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首都师范大学数学科学学院学术讲座

 

2016-10-08


时间:2016年9月21日(周三)4:00-5:00

地点:首都师大北二区教学楼508教室欢迎全体师生积极参加!

主办单位:首都师范大学数学科学学院首都师范大学数学与交叉科学研究院北京成像技术高精尖创新中心

报告人:江松 教授(Institute of Applied Physics and Computational Mathematics, Beijing, China)

 

简介:北京应用物理与计算数学研究所研究员,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。

 

摘要: We investigate the stabilizing effect of the vertical equilibrium magnetic field in the Rayleigh-Taylor (RT) problem for a nonhomogeneous incompressible viscous magnetohydrodynamic (MHD) fluid of zero resistivity in the presence of a uniform gravitational field in a horizontally periodic domain, in which the velocity of the fluid is non-slip on both upper and lower flat boundaries When an initial perturbation around a magnetic RT equilibrium state satisfies some relations, and the strength of the vertical magnetic field of the equilibrium state is bigger than the critical number we can use the Bogovskii function in the standing-wave form and adapt a two-tier energy method in Lagrangian coordinates to show the existence of  a unique global-in-time (perturbed) stability solution to the magnetic RT problem. For the case that the strength of the vertical magnetic field is smaller than the critical number, by developing new analysis techniques based on the method of bootstrap instability, we show that the nonlinear RT instability will occur.  The current result reveals from the mathematical point of view that the sufficiently large vertical equilibrium magnetic field has a stabilizing effect and can prevent the RT instability in MHD flows from occurring. Similar conclusions can be also verified for the horizontal magnetic field when the domain is vertically periodic. For the compressible MHD case, we shall discuss the Parker instability arising from astrophysics and also analyze the stabilizing effect of the magnetic fields.  (joint work with Fei Jiang)

 

(科技处 北京成像技术高精尖创新中心 供稿)