Seminario

Seminario Análisis y EDPs

On the stability of a point charge for the Vlasov-Poisson system

Ponente:  Klaus Widmayer (École polytechnique fédérale de Lausanne)
Fecha:  miércoles 24 de marzo de 2021 - 15:00
Lugar:   Online - Info: sites.google.com/view/analysis-pde-seminar

Resumen:
A point charge is a particularly basic and important equilibrium of the Vlasov-Poisson equations, and the study of its stability has inspired several major contributions. In this talk we present some recent work, which brings a fresh perspective on this problem. Our new approach combines a Lagrangian analysis of the linearized problem with an Eulerian PDE framework in the nonlinear analysis, all the while respecting the symplectic structure. As a result, for the case of radial initial data, we see that solutions are global and in fact disperse to infinity via a modified scattering along trajectories of the linearized flow. This is joint work with Benoit Pausader (Brown University).