# Analysis Seminar

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

**Speaker:**
Benoit Pausader, Brown University

**Location:**
Warren Weaver Hall 1302

**Date:**
Thursday, April 18, 2024, 11 a.m.

**Synopsis:**

We consider solutions of the repulsive Vlasov-Poisson systems 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 decay 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 (the flow of the 2-body ODE), 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 (Tongji U.).