Existence of a Local Solution to the Maxwell-Dirac-Coulomb Equations

Math Physics Seminar
Friday, March 16, 2018 - 15:00
1 hour (actually 50 minutes)
Skiles 202
School of Mathematics, Georgia Tech
Consider a relativistic electron interacting with a nucleus of nuclear charge Z and coupled to its self-generated electromagnetic field. The resulting system of equations describing the time evolution of this electron and its corresponding vector potential are known as the Maxwell-Dirac-Coulomb (MDC) equations. We study the time local well-posedness of the MDC equations, and, under reasonable restrictions on the nuclear charge Z, we prove the existence of a unique local in time solution to these equations.