Smoothing effects for Schrödinger equations with electro-magnetic potentials and applications to the Maxwell–Schrödinger equations

We consider Schrödinger equations in R1+2 with electro-magnetic potentials. The potentials belong to H1, and typically they are time-independent or determined as solutions to inhomogeneous wave equations. We prove Kato type smoothing estimates for solutions. We also apply this result to the Maxwell– Schrödinger equations in the Lorentz gauge and prove unique solvability of this system in the energy space. © 2012 Elsevier Inc. All rights reserved