Author(s)

Lukas Degu Petros

Department of Mathematics, Jimma University, Jimma, Ethiopia.

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.

Maxwell Equation, Vlasov Equation, Existence and Uniqueness

Petros, L. (2018) Existence and Uniqueness of Global Smooth Solutions for Vlasov Maxwell Equations. Advances in Pure Mathematics, 8, 45-76. doi: 10.4236/apm.2018.81005.