TITLE:
Existence and Uniqueness of Global Smooth Solutions for Vlasov Maxwell Equations
AUTHORS:
Lukas Degu Petros
KEYWORDS:
Maxwell Equation, Vlasov Equation, Existence and Uniqueness
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.1,
January
29,
2018
ABSTRACT: 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, the resulting theorem is proved by taking initial data , . A small data global existence result is presented
as well.