Energetic variational approaches for multiphase flow systems with phase transition

We study the governing equations for the motion of the fluid particles near air-water interface from an energetic point of view. Since evaporation and condensation phenomena occur at the interface, we have to consider phase transition. This paper applies an energetic variational approach to derive multiphase flow systems with phase transition, where a multiphase flow means compressible and incompressible two-phase flow. We also research the conservation and energy laws of our system. The key ideas of deriving our systems are to acknowledge the existence of the interface and to apply an energetic variational approach. More precisely, we assume that both the coefficient of surface tension and the density of the interface are constants, and we apply an energetic variational approach to look for the dominant equations for the densities of our multiphase flow systems with phase transition. As applications, we can derive the usual Euler and Navier-Stokes systems, or a two-phase flow system with surface tension by our methods.