About One Dimensional Viscous Liquid - Gas Two Phase Flow Model Of Classical Solutions Of The Global Existence And Asymptotic Behavior

In this paper, we mainly consider a one-dimensional viscous liquid-gas two-phase model. This model is frequently used to simulate unsteady, compressible flow of liquid and gas in pipes, The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic, and the initial masses is connected to vacuum with discontinuities. This is a free boundary value problem, The goal of this dissertation is to study some aspects of this model. It mainly achieved in the following aspects:1. The global existence of classical solutions for this model is studied, when the viscosity coefficient is constant. First, we prove the existence of local strong solutions by applying Lagrangian variables and the Schauder theory for lincar parabolic equations. Then, we extend local solutions to classical solutions by using a priori estimates and obtain a global existence result for classical solution.2. The asymptotic behavior of the mass functions near the interfaces sep-arating the gas from vacuum is also studied. By using the energy estimates, Sobolcv’s inequality, Gronwall’s inequality and Holder’s inequality, we obtain the asymptotic behavior of global classical solutions.