Nonlinear stability of Newtonian galaxies and stars from a mathematical perspective.
The stability of equilibrium configurations of galaxies or stars are time honored problems in astrophysics. We present mathematical results on these problems that have recently been obtained by Yan Guo and the author in the context of the Vlasov-Poisson and the Euler-Poisson models. Based on a careful analysis of the minimization properties of conserved quantities--the total energy and so called Casimir functionals--nonlinear stability results are obtained for a wide class of equilibria.