A mathematical theory of isolated systems in relativistic plasma physics
Abstract
The existence and the properties of isolated solutions to the relativistic VlasovMaxwell system with initial data on the backward hyperboloid $t=\sqrt{1+x^2}$ are investigated. Isolated solutions of VlasovMaxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the massenergy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the massenergy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the massenergy on the forward hyperboloids is nonincreasing and uniformly bounded by the massenergy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one dimensional version of the system.
 Publication:

arXiv eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:mathph/0606031
 Bibcode:
 2006math.ph...6031C
 Keywords:

 Mathematical Physics;
 35B40;
 35A05;
 35Q75
 EPrint:
 30 pages, no figures