Solutions of Euler-Poisson Equations in RN

In this article, the authors study the structure of the solutions for the Euler-Poisson equations in a bounded domain of Rn with the given angular velocity and n is an odd number. For a ball domain and a constant angular velocity, both existence and non-existence theorem are obtained depending on the adiabatic gas constant γ. In addition, they obtain the monotonicity of the radius of the star with both angular velocity and center density. They also prove that the radius of a rotating spherically symmetric star, with given constant angular velocity and constant entropy, is uniformly bounded independent of the central density. This is different to the case of the non-rotating star.