Georgia Institute of Technology College of Sciences

The three-dimensional Maxwell-Pauli-Coulomb (MPC) equations are a system of nonlinear, coupled partial differential equations describing the time evolution of a single electron interacting with its self-generated electromagnetic field and a static (infinitly heavy) nucleus of atomic number Z. The time local (and, hence, global) well-posedness of the MPC equations for any initial data is an open problem, even when Z = 0. In this talk we present some progress towards understanding the well-posedness of the MPC equations and, in particular, how the existence of solutions depends on the stability of the one-electron atom. Our main result is that time global finite-energy weak solutions to the MPC equations exist provided Z is less than a critical charge. This is an oral comprehensive exam. All are welcome to attend.