本文關鍵詞： 電流體力學 人工可壓逼近 正則準則 弱-L~p泛函　出處：《安徽大學》2017年碩士論文　論文類型：學位論文

【摘要】：流體力學是力學的一個重要分支,通常是由流體的質(zhì)量守恒,動量守恒等來描述.電流體力學主要研究的是電現(xiàn)象和流體力學現(xiàn)象的復合現(xiàn)象.在靜電起電機,宇宙火箭等領域的理論研究中起到重要的作用.對電流體力學方程解的存在唯一性,正則性,長時間漸進行為,吸引子的存在性及其維數(shù)估計等方面已做了大量的研究.自Chorin和Temam引進了人工可壓逼近方法以來,偏微分解的數(shù)值逼近引起人們越來越多的關注.本篇碩士畢業(yè)論文主要研究電流體力學的人工可壓逼近和弱-Lp Prodi-Serrin型正則準則.本篇論文共分為五章.在第一章中,主要給出電流體力學方程的背景知識和相關研究現(xiàn)狀.在第二章中,簡要給出了本文所涉及到的一些基本空間和重要不等式.在第三章中,考慮兩維有界開區(qū)域上的電流體力學方程的人工可壓逼近.證明了擾動的可壓電流體力學方程解的存在唯一性及其解收斂到原不可壓電流體力學方程的解.在第四章中,考察三維具有光滑邊界條件的有界開區(qū)域上電流體力學方程弱解的正則準則.證明了在條件（？）下，，弱解在區(qū)間[o,T]上也為強解在第五章中,對本文的工作進行了總結(jié),并給出了下一步的研究計劃.
[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.
【學位授予單位】：安徽大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175

【參考文獻】

相關期刊論文 前1條

1 ;A NEW REGULARITY CLASS FOR THE NAVIER-STOKES EQUATIONS IN IR~n[J];Chinese Annals of Mathematics;1995年04期

本文編號：1515897