  We consider the governing equations for the motion of the inviscid fluids in
two moving domains and an evolving surface from an energetic point of view. We
employ our energetic variational approaches to derive inviscid multiphase flow
systems with surface flow and tension. More precisely, we calculate the
variation of the flow maps to the action integral for our model to derive both
surface flow and tension. We also study the conservation and energy laws of our
multiphase flow systems. The key idea of deriving the pressure of the
compressible fluid on the surface is to make use of the feature of the
barotropic fluid, and the key idea of deriving the pressure of the
incompressible fluid on the surface is to apply a generalized Helmholtz-Weyl
decomposition on a closed surface.
