Nonlinear Stability of Newtonian Galaxies and Stars from a Mathematical Perspective

Abstract

The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems which have in recent years been obtained by Yan Guo and the author in the context of the Vlasov-Poisson and the Euler-Poisson model. Based on a careful analysis of the minimization properties of conserved quantities--the total energy and so-called Casimir functionals--non-linear stability results are obtained for a wide class of equilibria.

arXiv comment18 pages, LaTeX

References in corpus (6)

• Non-linear stability of gaseous stars
• Stable steady states in stellar dynamics
• Isotropic steady states in galactic dynamics revised
• Flat steady states in stellar dynamics - existence and stability
• Stable Models of Elliptical Galaxies
• Stability of spherically symmetric steady states in galactic dynamics against general perturbations

Cited by in corpus (6)

• A numerical investigation of the stability of steady states and critical phenomena for the spherically symmetric Einstein-Vlasov system
• A non-variational approach to nonlinear stability in stellar dynamics applied to the King model
• Relative equilibria in continuous stellar dynamics
• A logarithmic Hardy inequality
• Equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model
• Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the gravitational case