| The Navier-Stokes equations reflect the basic mechanical law of viscous fluid flow,which is of great significance in hydrodynamics.In this paper,a diffusion interface model for describing the motion of complex fluid is studied,in the case of incompressible isothermal,ignoring chemical reaction and other external forces,the model is simplified as the coupling of the Navier-Stokes equations for fluid velocity and Cahn-Hilliard model controlling phase parameters,which is Cahn-HilliardNavier-Stokes equations.Due to the influence of various unstable factors,the fluid motion will generate stochastic fluctuations,and this fluctuation is regarded as a stochastic phenomenon.It is reasonable to add different types of stochastic terms to the equations to characterize uncertainties.Therefore,this paper mainly studies the Cahn-Hilliard-Navier-Stokes equations under stochastic disturbances.This paper uses stochastic analysis,partial differential equation theory,and infinite-dimensional dynamic system theory to study the well-posedness of the two-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations under different conditions.The content is as follows:The first chapter introduces the research background,research significance,research status of this article,and gives the relevant basic knowledge.The second chapter studies the well-posedness of the two-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations driven by Lévy noise.The premise of the well-posedness of the two-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations driven by the Gaussian noise.Galerkin approximation and uniform estimates are used to prove the well-posedness of the equations under Lévy noise.In the third chapter,using iterative techniques,uniform estimates,and weak convergence to study the well-posedness of the two-dimensional stochastic Cahn-Hilliard-Navier-Stokes equations under non-Lipschitz conditions.The fourth chapter studies the regularity of the solutions to the equations,using It? formula,a prior estimates to generalize the solutions to a more regularity space. |
