Abstract

The Vlasov-Poisson system with massless electrons (VPME) is widely used in plasma physics to model the evolution of ions in a plasma. It differs from the Vlasov-Poisson system (VP) for electrons in that the Poisson coupling has an exponential nonlinearity that creates several mathematical difficulties. In particular, while global well-posedness in 3 D is well understood in the electron case, this problem remained completely open for the ion model with massless electrons. The aim of this paper is to fill this gap by proving uniqueness for VPME in the class of solutions with bounded density, and global existence of solutions with bounded density for a general class of initial data, generalising all the previous results known for VP.

摘要

具有无质量电子 (VPME) 的 Vlasov-Poisson 系统广泛用于等离子体物理学，以模拟等离子体中离子的演化。它与电子的 Vlasov-Poisson 系统 (VP) 的不同之处在于，泊松耦合具有指数非线性，这会产生一些数学难题。特别是，虽然 3D 中的全局适定性在电子情况下很好理解，但对于具有无质量电子的离子模型，这个问题仍然完全开放。本文的目的是通过证明 VPME 在具有有界密度的解类中的唯一性，以及对于一般初始数据类具有有界密度的解的全局存在，来填补这一空白，概括所有先前已知的 VP 结果。