Continuation Criteria for the Relativistic Vlasov-Maxwell System

The relativistic Vlasov-Maxwell system models the evolution of a collisionless plasma (completely ionized gas) and is a system of coupled nonlinear wave and kinetic transport equations. It remains an open problem to prove global existence and uniqueness of solutions to this system in three-dimensional space. We will discuss the progress on this problem and techniques such as Strichartz estimates for the wave equation, interpolation inequalities and conservation laws.