The Vlasov-Maxwell-Fokker-Planck system in two space dimensions

摘要

We consider the Cauchy problem for the Vlasov-Maxwell-Fokker-Planck system in the plane. It is shown that for smooth initial data, as long as the electromagnetic fields remain bounded, then their derivatives do also. Glassey and Strauss have shown this to hold for the relativistic Vlasov-Maxwell system in three dimensions, but the method here is totally different. In the work of Glassey and Strauss, the relativistic nature of the particle transport played an essential role. In this work, the transport is nonrelativistic, and smoothing from the Fokker-Planck operator is exploited. Copyright (c) 2015John Wiley & Sons, Ltd.