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5月12日学术报告:On global dynamics of 3-dim incompressible MHD with arbitrary small diffusion

作者:admin 点击:616 发布时间:2016-5-11 14:49:39

报告人:何凌冰 副教授 (清华大学数学科学系)
报告时间:2016年5月12日 14:00—15:00。 
报告地点:理学院547
报告人简介:
何凌冰,男,2007年毕业于中科院数学与系统科学研究院,导师:张平 研究
员。主要研究方向是:Boltzmann,Landau方程的适定性,长时间行为和方程
间的渐近分析;Navier-Stokes方程的稳定性理论和MHD系统的波动现象。
摘要:
We construct and study global solutions for the 3-dimensional 
incompressible MHD systems with arbitrary small viscosity. 
In particular,we provide a rigorous justification for the fol-
lowing dynamical phenomenon observed in many contexts: the 
solution at the beginning behave like non-dispersive waves and 
the shape of the solution persists for a very long time 
(proportional to the Reynolds number); thereafter, the solution 
will be damped due to the long-time accumulation of the diffu-
sive effects; eventually, the total energy of the system becomes 
extremely small compared to the viscosity so that the diffusion 
takes over and the solution afterwards decays fast in time. We 
do not assume any symmetry condition. The size of data and the a 
priori estimates do not depend on viscosity. The proof is builded 
upon a novel use of the basic energy identity and a geometric 
study of the characteristic hypersurfaces. The approach is partly 
inspired by Christodoulou-Klainerman’s proof of the nonlinear 
stability of Minkowski space in general relativity. This is a joint 
work with Li XU (Chinese Academy of Sciences) and Pin YU (Tsinghua 
University). 
 
 
 
 
 
 
 
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