Regularity of hyperbolic magnetic Schrödinger equation with oscillating coefficients

Abstract

This paper mainly discusses the regularity of hyperbolic magnetic Schrödinger equation with singular coefficients near the origin. We apply the techniques from microlocal analysis to explore the upper bound of loss of regularity. Furthermore, in order to demonstrate the optimality of the result, a delicate counterexample with periodic coefficients will be constructed to show the lower bound of loss of regularity by the application of harmonic analysis and instability arguments.