Propagation of the Gabor Wave Front Set for Schrödinger Equations with non-smooth potentials

Abstract

We consider Scrödinger equations with real-valued smooth Hamiltonians, and non-smooth bounded pseudo-differential potentials, whose symbols may be not even differentiable. The well-posedness of the Cauchy problem is proved in the frame of the modulation spaces, and results of micro-local propagation of singularities are given in terms of Gabor wave front sets.

arXiv comment34 pages