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

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.