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

In this paper,we study the movement of compressible two-phase flow with diffusion interfaces,which is called Navier-Stokes/Allen-Cahn equations.For the initial phase field with phase transition,we obtain the existence and uniqueness of global strong solutions to the Cauchy problem under the assumptions of small initial perturbations.To prove the conclusion,we mainly use the energy estimation method combined with the fixed-point theorem.The conclusion indicates that the kind of immiscible two-phase flow can’t occur vacuum and phase separation in finite time.