Small Alfvén number limit for incompressible magneto-hydrodynamics in a domain with boundaries  

作　　者：Song Jiang Qiangchang Ju Xin Xu 

机构地区：[1]Institute of Applied Physics and Computational Mathematics

出　　处：《Science China Mathematics》2019年第11期2229-2248,共20页中国科学：数学（英文版）

基　　金：supported by the Israel Science Foundation-National Natural Science Foundation of China Joint Research Program (Grant No. 11761141008);supported by the National Basic Research Program of China (Grant No. 2014CB745002);National Natural Science Foundation of China (Grant No. 11631008);supported by National Natural Science Foundation of China (Grant Nos. 11571046, 11471028 and 11671225);Beijing Natural Science Foundation (Grant No. 1182004)

摘　　要：For any fixed Alfvén number, the local well-posedness is proved for the equations of threedimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfvén number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfvén number goes to zero.For any fixed Alfvén number, the local well-posedness is proved for the equations of threedimensional ideal incompressible magneto-hydrodynamics in a domain with boundaries. Under appropriate conditions, a smooth solution is shown to exist in a time interval independent of the Alfvén number, and the solutions of the original system tend to the solutions of a two-dimensional Euler flow coupled with a linear transport equation as the Alfvén number goes to zero.

关 键 词：MHD equations VANISHING Alfvén NUMBER LIMIT SMALL Mach NUMBER uniform estimates 

分 类 号：O17[理学—数学]