Some Research On Navier-Stokes-Voight Equation

In this paper,the Navier-Stokes-Voight(NSV)equation has been studied,which proposed as a model for a viscoelastic incompressible fluid by Oskolkov in 1973.Firstly,we concern the exact solution of one dimensional Navier-Stokes-Voight equa-tion.Secondly,the well-posedness of three dimensional stochastic Navier-Stokes-Voi-ght equation and the existence of invariant measure were studied.While compared wi-th the determined Navier-Stokes-Voight equation.by adding the term of multiplicative noise,stochastic Navier-Stokes-Voight equation is suitable for more general turbulences.It has abroad application in meteorology,geophysics,biology.This paper is divided into three chapters.In chapter one.we mainly introduce the research background of Navier-Stokes-Voight equation and its development,at the same time,we do some preparation for the paper.In chapter two.by the symmetry of lie group,we solve the Lie equation and find operators admitted by the Navier-Stokes-Voight equation.Finally we provide one of the exact solution of one dimensional Navier-Stokes-Voight equation.In chapter three,we introduce stochastic Navier-Stokes-Voight equation By using energy estimate,compactness theory in partial differential equation and sto-chastic analysis theory,we proved the well-posedness of the stochastic Navier-Stokes-Voight equation in R3.In chapter four,by means of ergodicity and probality measure,we study the in-variant measure of Stochastic Navier-Stokes-Voight equation.In the end,we comp-lete the provement of existence of invariant measure for stochastic Navier-Stokes-Vo-ight equation.