%0 Journal Article
%T Existence and Uniqueness of Global Smooth Solutions for Vlasov Maxwell Equations
%A Lukas Degu Petros
%J Advances in Pure Mathematics
%P 45-76
%@ 2160-0384
%D 2018
%I Scientific Research Publishing
%R 10.4236/apm.2018.81005
%X Global existence of classical solutions to the
relativistic Vlasov-Maxwell system, given sufficiently regular initial data, is
a long-standing open problem. The aim of this project is to present in details
the results of a paper published in 1986 by Robert Glassey and Walter Strauss.
In that paper, a sufficient condition for the global existence of a smooth
solution to the relativistic Vlasov-Maxwell system is derived. In the following</span><span style=\"font-family:Verdana;\">,</span><span style=\"font-size:10pt;font-family:&quot;\"><span style=\"font-family:Verdana;font-size:12px;\"> the resulting theorem is proved by taking initial data </span><img src=\"Edit_15854804-14a7-4920-bf9a-f1f2407dc76e.bmp\" alt=\"\" /></span><span style=\"font-size:10pt;font-family:&quot;\"></span><span style=\"font-size:10pt;font-family:&quot;\"><span style=\"font-family:Verdana;font-size:12px;\">, </span><img src=\"Edit_1b28c3fd-3986-482e-bffa-2472cd4e15a5.bmp\" alt=\"\" /></span><span style=\"font-size:10pt;font-family:&quot;\"></span><span style=\"font-family:Verdana;\">. A small data global existence result is presented
as well.
%K Maxwell Equation
%K Vlasov Equation
%K Existence and Uniqueness
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=82079