On generalized compressible fluid systems on an evolving surface with a boundary

Abstract

We consider compressible fluid flow on an evolving surface with a smooth boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make mathematical models for compressible fluid flow on the evolving surface. Moreover, we investigate the boundary conditions in co-normal direction for our fluid systems to study the conservation and energy laws of the systems.