不可压磁流体方程强解的整体存在性
发布时间：2019-05-29 23:45
【摘要】：本文的主要研究3维不可压MHD(Magnetohydrodynamic)方程强解的整体存在性及应用时间分段估计的方法研究带有大外力的3维不可压MHD方程强解的整体存在性。全文分成以下三部分,即:第一部分:介绍3维不可压MHD方程强解的研究背景、研究现状以及进行证明所用到一些重要理论和不等式等基本知识。第二部分:研究3维不可压MHD方程强解的整体存在性的问题,在Kim和Craig等等研究成果的基础上,在不弱化小初值条件下,通过使方程的质量或者密度适当小时或粘性系数足够大时,从而得到方程存在整体强解。第三部分:研究3维不可压MHD方程在带有大外力的情况下强解的存在性问题,在前人已证明3维不可压MHD方程强解局部存在性的研究成果上,结合时间分段估计证明方法,从而得到带有大外力的3维不可压MHD方程强解的整体存在性。
[Abstract]:In this paper, we mainly study the global existence of strong solutions for 3-dimensional incompressible MHD (Magnetohydrodynamic) equations and the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces by using the method of time piecewise estimation. The full text is divided into the following three parts: in the first part, the research background, research status and some important theories and inequalities used to prove the strong solution of three-dimensional incompressible MHD equation are introduced. In the second part, we study the global existence of strong solutions for 3-dimensional incompressible MHD equations. on the basis of Kim and Craig's research results, without weakening the small initial value, By making the mass or density of the equation small enough or when the viscosity coefficient is large enough, the global strong solution of the equation is obtained. In the third part, the existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is studied. on the basis of the previous research results on the local existence of strong solutions for 3-dimensional incompressible MHD equations, combined with the time piecewise estimation method, Thus, the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is obtained.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2488323
[Abstract]:In this paper, we mainly study the global existence of strong solutions for 3-dimensional incompressible MHD (Magnetohydrodynamic) equations and the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces by using the method of time piecewise estimation. The full text is divided into the following three parts: in the first part, the research background, research status and some important theories and inequalities used to prove the strong solution of three-dimensional incompressible MHD equation are introduced. In the second part, we study the global existence of strong solutions for 3-dimensional incompressible MHD equations. on the basis of Kim and Craig's research results, without weakening the small initial value, By making the mass or density of the equation small enough or when the viscosity coefficient is large enough, the global strong solution of the equation is obtained. In the third part, the existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is studied. on the basis of the previous research results on the local existence of strong solutions for 3-dimensional incompressible MHD equations, combined with the time piecewise estimation method, Thus, the global existence of strong solutions for 3-dimensional incompressible MHD equations with large external forces is obtained.
【学位授予单位】：华侨大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 ;Global Smooth Solutions to the 2-D Inhomogeneous Navier-Stokes Equations with Variable Viscosity[J];Chinese Annals of Mathematics;2009年05期
，本文编号：2488323
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