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Two-component viscous flows with density-dependent transition layer. (English) Zbl 1194.35314

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.

MSC:

35Q30 Navier-Stokes equations
76T10 Liquid-gas two-phase flows, bubbly flows
76N99 Compressible fluids and gas dynamics
92B99 Mathematical biology in general
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