Stability of a point charge for the repulsive Vlasov-Poisson system

Benoit Pausader, Brown University
Fine Hall 314

We consider solutions of the repulsive Vlasov-Poisson system which are a combination of a point charge and a small density with respect to Liouville measure (a ``cloud''), and we show that these solutions exist globally, that the electric field decays at an optimal rate and that the particle distribution converges along a modified scattering dynamics. This follows by a Lagrangian study of the linearized equation, which is integrated by means of an asymptotic action-angle coordinate transformation, and an Eulerian study of the nonlinear dynamic which exhibits the ``mixing'' mechanism responsible for the asymptotic behavior.

This is joint work with Klaus Widmayer (U. Zurich) and Jiaqi Yang (ICERM).