Global Existence for the Vlasov-Poisson System with Steady Spatial Asymptotics |
| |
Authors: | Stephen Pankavich |
| |
Institution: | 1. Department of Mathematical Sciences , Carnegie Mellon University , Pittsburgh, Pennsylvania, USA sdp@andrew.cmu.edu |
| |
Abstract: | ABSTRACT A collisionless plasma is modelled by the Vlasov-Poisson system in three space dimensions. A fixed background of positive charge—dependant upon only velocity—is assumed. The situation in which mobile negative ions balance the positive charge as | x | → ∞ is considered. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior for large | x |, which were previously shown to exist locally in time, are continued globally. This is done by showing that the charge density decays at least as fast as | x |?6. This article also establishes decay estimates for the electrostatic field and its derivatives. |
| |
Keywords: | Cauchy problem Global existence Kinetic theory Spatial decay Vlasov |
|
|