Electro-hydrodynamics方程的可压逼近与正则准则

发布时间：2018-02-16 16:02

本文关键词： 电流体力学人工可压逼近正则准则弱-L~p泛函　出处：《安徽大学》2017年硕士论文　论文类型：学位论文

【摘要】：流体力学是力学的一个重要分支,通常是由流体的质量守恒,动量守恒等来描述.电流体力学主要研究的是电现象和流体力学现象的复合现象.在静电起电机,宇宙火箭等领域的理论研究中起到重要的作用.对电流体力学方程解的存在唯一性,正则性,长时间渐进行为,吸引子的存在性及其维数估计等方面已做了大量的研究.自Chorin和Temam引进了人工可压逼近方法以来,偏微分解的数值逼近引起人们越来越多的关注.本篇硕士毕业论文主要研究电流体力学的人工可压逼近和弱-Lp Prodi-Serrin型正则准则.本篇论文共分为五章.在第一章中,主要给出电流体力学方程的背景知识和相关研究现状.在第二章中,简要给出了本文所涉及到的一些基本空间和重要不等式.在第三章中,考虑两维有界开区域上的电流体力学方程的人工可压逼近.证明了扰动的可压电流体力学方程解的存在唯一性及其解收敛到原不可压电流体力学方程的解.在第四章中,考察三维具有光滑边界条件的有界开区域上电流体力学方程弱解的正则准则.证明了在条件（？）下，，弱解在区间[o,T]上也为强解在第五章中,对本文的工作进行了总结,并给出了下一步的研究计划.
[Abstract]:Fluid mechanics is an important branch of mechanics, which is usually described by the conservation of fluid mass and momentum. It plays an important role in the theoretical research of space rocket and other fields. The existence, uniqueness, regularity, long term asymptotic behavior of the solution to the electrohydrodynamic equation, A great deal of research has been done on the existence and dimension estimation of attractors. Since the introduction of artificial compressible approximation methods by Chorin and Temam, The numerical approximation of partial differential decomposition has attracted more and more attention. In this thesis, the artificial compressible approximation and weak LP Prodi-Serrin type canonical criteria of electrohydrodynamics are studied. The thesis is divided into five chapters. In the first chapter, In chapter 2, some basic spaces and important inequalities involved in this paper are briefly given. In this paper, we consider the artificial compressible approximation of electrohydrodynamic equations in two dimensional bounded open domain. We prove the existence and uniqueness of the solutions of perturbed piezoelectric hydrodynamic equations and their convergence to the solutions of the original unpiezoelectric hydrodynamic equations. In Chapter 4th, The canonical criteria for weak solutions of electrohydrodynamic equations in a bounded open domain with smooth boundary conditions are investigated. In chapter 5th, the weak solution is also a strong solution on interval [OT]. In chapter 5th, the work of this paper is summarized and the next research plan is given.
【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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