Strong Lagrangian Solutions of the (Relativistic) Vlasov--Poisson System for NonSmooth, Spherically Symmetric Data

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.