On the Dynamics of Liquid-Vapor Phase Transition

We consider a multidimensional model for the dynamics of liquid-vapor phase transitions. In the present context, liquid and vapor are treated as different species with different volume fractions and different molecular weights. The model presented here is a prototype of a “binary fluid mixture” and is formulated by a system that generalizes the Navier–Stokes(–Fourier) equations in Eulerian coordinates. This system takes now a new form due to the choice of rather complex constitutive relations that can accommodate appropriately the physical context. The setting of the problem presented in this work is motivated by physical considerations. The transport fluxes satisfy rather general constitutive laws, the viscosity and heat conductivity depend on the temperature, and the pressure law is a nonlinear function of the temperature depending on the mass density fraction of the vapor (liquid) in the fluid as well as the molecular weights of the individual species. The existence of globally defined weak solutions o...

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