The Existence And Uniqueness Of Solutions To The Cauchy Problem For Compressible Navier-Stokes/Cahn-Hilliard Equations In 3-D

In this paper,we mainly discuss and study the flow problem of a class of insoluble two-phase fluid with diffusion interface,which is described by Navier-Stokes/Cahn-Hilliard equations.Firstly,we can use linearization method and classical Schauder fixed point theory to obtain the existence and uniqueness of the local solutions of the equations.Then,under the condition of initial small perturbation,we get the uniform prior estimation of the solution of the equation by using the method of energy estimation.Base on the existence and uniqueness of the local solution,the solution is extended,and finally the equation has a unique strong solution.The results show that the phase separation state remains unchanged in the case of small perturbation.