Local well-posedness of the Vlasov-Poisson-Landau system and related models

TL;DR

This paper establishes local well-posedness for the Vlasov-Poisson-Landau system and its massless electron variant in 3D periodic domains, using weighted anisotropic Sobolev norms, extending prior work with Yan Guo.

Contribution

It proves local existence and uniqueness for large initial data in the Vlasov-Poisson-Landau system and analyzes the massless electron variant, advancing mathematical understanding of these plasma models.

Findings

Proved local well-posedness for the Vlasov-Poisson-Landau system.

Extended analysis to the massless electron system and Poincare-Poisson system.

Utilized weighted anisotropic Sobolev norms for the proofs.

Abstract

We prove local well-posedness for the Vlasov-Poisson-Landau system and the variant with massless electrons in a 3D periodic spatial domain for large initial data. This is accomplished by propagating weighted anisotropic L2-based Sobolev norms. In the case of the massless electron system, we also carry out an analysis of the Poincare-Poisson system. This is a companion paper to the author's previous work with Yan Guo.