Strong Lagrangian solutions of the (relativistic) Vlasov-Poisson system for non-smooth, spherically symmetric data

TL;DR

This paper establishes local existence and uniqueness of Lagrangian solutions for the non-relativistic and relativistic Vlasov-Poisson systems with non-smooth, spherically symmetric data, ensuring conservation laws and stability analysis applicability.

Contribution

It introduces a framework for solutions that are valid for non-smooth data, extending the analysis to relativistic cases with spherical symmetry.

Findings

Solutions preserve standard conserved quantities.

Solutions are constant along characteristic flows.

Global existence in the non-relativistic case.

Abstract

We prove a local existence and uniqueness result for the non-relativistic and relativistic Vlasov-Poisson system for data which need not even be continuous. The corresponding solutions preserve all the standard conserved quantities and are constant along their pointwise defined characteristic flow so that these solutions are suitable for the stability analysis of not necessarily smooth steady states. They satisfy the well-known continuation criterion and are global in the non-relativistic case. The only unwanted requirement on the data is that they be spherically symmetric.