The Compressibility Approximation And Regularity Criteria Of Electro-hydrodynamics System

The fluid dynamics is an important branch of dynamics,which is usu-ally described by the mass conservation,momentum conservation and so on.Electro-hydrodynamics mainly studies the phenomena of electric phenomena and dynamics phenomenon,which plays an important role in the field of the research on the electrostatic generator and the rocket.Recently,the existences,uniqueness,regularity,the long-time behavior of solution and existences,di-mension of attractor for the electro-hydrodynamics system have been stud-ied largely.Since Chorin and Temam introduced the artificial compressibility method,scholars pay more and more attention to numerical solution of partial differential equations.In this master's thesis,we are mainly devoted to study-ing the artificial compressibility approximation and weak-Lp Prodi-Serrin type regularity criteria of several electro-hydrodynamics system.This paper is divided into five chapters.In Chapter one,we sketch some background knowledge and related research of the electro-hydrodynamics sys-tem.In Chapter two,we provide some basic spaces and important inequalities which are involved in this paper.In Chapter three,we consider the artificial compressibility approximation of the electro-hydrodynamics system on the open bounded smooth domain in R2.We prove the unique existence and convergence of solutions for the perturbed compressible electro-hydrodynamics system to the solutions of the incompress-ible electro-hydrodynamics system.In Chapter four,we investigate the regularity criteria for weak solution of the electro-hydrodynamics system on the open bounded domain with smooth boundary.We show that the solution (u,n,p,?) remains strong on [0,T](?)depending only on r and ?.In Chapter five,we summarize the work of this paper and give the further research plan.