可压缩磁流体动力学方程（MHD）解的研究

发布时间：2018-07-12 19:23

本文选题：磁流体方程 + 稳态解　；参考：《上海师范大学》2015年硕士论文

【摘要】：本论文研究的是带有外力的三维可压缩粘性磁流体方程(MHD),首先推导出相应稳态方程的非恒定稳态解的存在性,然后,当初值和稳态解很接近时,可以得到三维可压缩粘性磁流体方程(MHD)整体解的存在性和衰减估计.本文的主要安排如下：第一章,主要介绍所研究课题的来源、发展历史、研究现状以及本文所讨论的主要问题.第二章,为本文中第四章的证明做一些预备工作.结合Lorentz空间的性质来分析线性磁流体方程解的一些基本估计.第三章,结合线性方程解的存在性,利用压缩映射原来证明稳态解的存在性,再建立先验估计来证明整体解存在性.第四章,在第二章的基础上分析整体解的衰减估计.
[Abstract]:In this paper, the three-dimensional compressible viscous magnetic fluid equation (MHD) with external force is studied. First, the existence of the unsteady steady state solution of the corresponding steady state equation is derived. Then, the existence and attenuation estimation of the global solution of the three-dimensional compressible viscous magnetic fluid equation (MHD) can be obtained when the initial value is close to the steady state solution. The main arrangement of this paper is in this paper. The first chapter mainly introduces the source of the subject, the history of the development, the present situation and the main problems discussed in this paper. The second chapter, for the proof of the fourth chapters in this article, is to do some preliminary work. The basic estimation of the solution of the linear magnetic fluid equation is analyzed in the light of the properties of the Lorentz space. The third chapter combines the solution of the linear equation. In the fourth chapter, the attenuation estimation of the global solution is analyzed on the basis of the second chapter.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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