Existence and Non-linear Stability of Rotating Star Solutions of the Compressible Euler–Poisson Equations

• Published in: Archive for rational mechanics and analysis 2009-03, Vol.191 (3), p.447-496
• Main Authors: Luo, Tao, Smoller, Joel
• Format: Article
• Language: English
• Subjects: Astronomy; Classical Mechanics; Complex Systems; Earth, ocean, space; Exact sciences and technology; Fluid dynamics; Fluid- and Aerodynamics; Fundamental areas of phenomenology (including applications); General theory; Mathematical and Computational Physics; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Physics and Astronomy; Stars; Stellar characteristics and properties; Stellar rotation; Studies; Theoretical
• ISSN: 0003-9527; 1432-0673
• DOI: 10.1007/s00205-007-0108-y

We prove the existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler–Poisson (Euler–Poisson) equations in three spatial dimensions with prescribed angular momentum and total mass. This problem can be formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having less symmetry than those functions considered in the classical Auchmuty–Beals paper. We prove the non-linear dynamical stability of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove finite time stability of solutions where the perturbations are entropy-weak solutions of the Euler–Poisson equations. Finally, we give a uniform (in time) a priori estimate for entropy-weak solutions of the Euler–Poisson equations.