Existence of Rotating Stars with Variable Entropy

Abstract

We model a rotating star as a compressible fluid subject to gravitational forces. In most of the mathematical literature the entropy is considered to be constant. Here we allow it to be variable. We consider a star that steadily rotates differentially around a fixed axis, say the zaxis. We prove the existence of a family of such stars with small angular velocity ω and small entropy s and with an equation of state p = Ke s ρ γ . Our analysis reduces to a hyperbolic equation for the entropy coupled to an elliptic equation for the density, together with a mass constraint.