Two-component viscous flows with density-dependent transition layer (Q846251)

This paper deals with a model for a flow with a phase change caused by chemical reactions in the material flow. The author studies the dynamics of a fluid structure as well as the dynamics of a phase field structure. The one-dimensional, non stationary, compressible Navier-Stokes system is coupled with a phase field equation of Allen-Cahn type, describing the development of a phase change in the material. The boundary of the flow domain, which depends on the time variable, contains a fixed part and a free boundary, representing the interface between the liquid or gaseous medium and the vacuum. The problem is studied for a density-dependent viscosity and for a density-dependent transition layer. Under some assumptions, the existence of a unique weak global solution is proved.