不可压MHD系统的零耗散极限中的边界层

发布时间：2018-03-09 15:11

本文选题：不可压的黏性扩散MHD方程　切入点：理想的不可压MHD方程　出处：《中国科学:数学》2017年10期 　论文类型：期刊论文

【摘要】：本文研究通常的Dirichlet物理边界条件下带有小而变化的黏性和磁扩散系数的不可压磁流体(MHD)方程组的初边值的极限问题;发现了一类非平凡的初值,对于这类初值能建立其Prandtl型边界层的一致稳定性,并且严格证明了理想的MHD方程组的解和Pandtl型边界层矫正子的叠加是黏性扩散不可压MHD方程的解的一致逼近.这里的主要困难是处理和控制由耗散的MHD系统和理想MHD系统边界条件差异产生的Prandtl型的奇异边界层.关键的观察是对于本文研究的初值,其解的速度场和磁场的边界层的主要奇异项存在有抵消现象.这使得我们能基于精细的能量方法来使用这个特殊结构带来的好处,从而克服在研究这类问题中通常不能解决的困难.此外,在黏性系数为固定的正常数情形,对于一般初值,也能建立磁场的扩散边界层的稳定性以及零磁扩散极限中解的一致收敛性.
[Abstract]:In this paper, we study the limit problem of the initial and boundary values of the incompressible magnetic fluid (Dirichlet) equations with small and variable viscosity and magnetic diffusion coefficient under the usual physical boundary conditions, and find a class of nontrivial initial values. For this kind of initial value, the uniform stability of the Prandtl type boundary layer can be established. It is proved strictly that the solution of ideal MHD equations and the superposition of Pandtl type boundary layer correctors are uniform approximations of solutions of viscous diffusion incompressible MHD equations. The main difficulty here is to deal with and control the solution of dissipative MHD systems and ideals. The singular boundary layer of Prandtl type produced by the difference of boundary conditions of MHD system. The key observation is the initial value of this paper. The main singularity in the boundary layer of the velocity field and the magnetic field is counteracted, which allows us to use the benefits of this particular structure based on the refined energy method. In addition, in the case of a normal number with a fixed viscosity coefficient, for a general initial value, The stability of the diffusion boundary layer of the magnetic field and the uniform convergence of the solution in the zero magnetic diffusion limit can also be established.
【作者单位】：北京工业大学应用数理学院;香港中文大学数学科学研究所;
【基金】：国家自然科学基金(批准号:11371042) 郑格如基金香港RGC Earmarked研究基金(批准号:CUHK-14305315和CUHK4048/13P) NSFC/RGC联合研究计划(批准号:N-CUHK443-13) 香港中文大学聚焦区域基金资助项目
【分类号】：O175

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