Relative Equilibria in Continuous Stellar Dynamics

Abstract

We study a three dimensional continuous model of gravitating matter rotating at constant angular velocity. In the rotating reference frame, by a finite dimensional reduction, we prove the existence of non radial stationary solutions whose supports are made of an arbitrarily large number of disjoint compact sets, in the low angular velocity and large scale limit. At first order, the solutions behave like point particles, thus making the link with the relative equilibria in N -body dynamics.

Stability of a Point Charge for the Vlasov–Poisson System: The Radial Case

“…We hope that the methods introduced in this work provide a template for the analysis of a large class of (collisionless) kinetic problems, for which the linearized equation is given as transport by a completely integrable ODE whose trajectories are open. 6 To be concrete we highlight some examples to this effect and further related open problems, on which we hope the analysis developed here can shed some new light:…”

“…The natural starting point here is the case of two charges surrounded by a gas, which already at the linear level brings the (restricted) 3-body problem into play. We refer to [6,28] for works in this direction for Vlasov-Poisson and related equations. (3) We believe that the Vlasov-Poisson evolution of measures which are not absolutely continuous with respect to Liouville is an interesting general problem which merits further investigation.…”

Travelling and rotating solutions to the generalized inviscid surface quasi-geostrophic equation

“…In [6] a related problem in gravitation theory, consisting in the desingularization of rotating point masses in a continuous model of stellar dynamics, has been considered. The result obtained there is similar to Theorem 1.5 for s = 1 2 .…”