Dynamical Behavior For A Class Of Stochastic Fluid Equations Driven By Nonlinear Noise

This thesis mainly studies the dynamic behavior of stochastic nonautonomous incompressible non-Newtonian fluid and stochastic 2)-Navier Stokes equation driven by nonlinear noise.Firstly,the mean random dynamical system generated by stochastic nonautonomous incompressible non-Newtonian fluid is studied.Secondly,the existence of the weak pullback mean random attractor of the equation in Bochner space is proved.Furthermore,the mean random dynamical system generated by the random 2)-Navier Stokes equation driven by nonlinear noise is studied.The existence of the weak pullback mean random attractor in Bochner space is also proved.Finally,the existence of invariant measures for stochastic 2)-Navier Stokes equations driven by nonlinear noise is established.This thesis is organized as follows:In Chapter 1,The research background of stochastic non-autonomous incompressible nonNewtonian fluid driven by nonlinear noise is introduced,and the main work of this thesis is briefly stated.In Chapter 2,The concepts and theorems of mean random dynamical system and mean random attractor are given.In Chapter 3,The mean random dynamical system generated by stochastic nonautonomous incompressible non-Newtonian fluid driven by nonlinear noise is studied and the existence of weak pullback mean random attractor of the equation in Bochner space is proved.In Chapter 4,The existence of weak pullback mean random attractors for stochastic 2)-Navier Stokes equations driven by nonlinear noise in Bochner space is proved.In Chapter 5,The existence of invariant measures for stochastic 2)-Navier Stokes equations driven by nonlinear noise is proved.