本文選題：磁流體方程 + 穩(wěn)態(tài)解　； 參考：《上海師范大學》2015年碩士論文

【摘要】：本論文研究的是帶有外力的三維可壓縮粘性磁流體方程(MHD),首先推導出相應穩(wěn)態(tài)方程的非恒定穩(wěn)態(tài)解的存在性,然后,當初值和穩(wěn)態(tài)解很接近時,可以得到三維可壓縮粘性磁流體方程(MHD)整體解的存在性和衰減估計.本文的主要安排如下：第一章,主要介紹所研究課題的來源、發(fā)展歷史、研究現(xiàn)狀以及本文所討論的主要問題.第二章,為本文中第四章的證明做一些預備工作.結合Lorentz空間的性質來分析線性磁流體方程解的一些基本估計.第三章,結合線性方程解的存在性,利用壓縮映射原來證明穩(wěn)態(tài)解的存在性,再建立先驗估計來證明整體解存在性.第四章,在第二章的基礎上分析整體解的衰減估計.
[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.
【學位授予單位】：上海師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O175

【參考文獻】

相關期刊論文 前1條

1 錢建貞;尹慧;;CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL FORCES[J];Acta Mathematica Scientia;2009年05期

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本文編號：2118226