The hard phase model is a relativistic fluid model in which the
fluid is assumed to be irrotational and the sound speed is assumed to be
equal to the the speed of light. During gravitational collapse of the
degenerate core of a massive star, the mass-energy density exceeds the
nuclear saturation density and the sound speed approaches the speed of
light. The hard phase is an idealized model for this physical situation.
In this talk, I will discuss recent work on the well-posedness of the hard
phase model with vacuum free boundary in the Minkowski background, and
extensions to the more general case of barotropic fluids with free
boundary. This is joint work with Shuang Miao and Sijue Wu.