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This paper mainly discuss the regularity behavior of the hyperbolic magneticSchroedinger equation with singular coefficients near the origin. We apply thetechniques from the microlocal analysis to explore the upper bound of loss ofregularity. Furthermore, in order to demonstrate the optimality of the result,a delicate counterexample with periodic coefficients will be constructed toshow the lower bound of loss of regularity by the application of harmonicanalysis and instability arguments.

Regularity of hyperbolic magnetic Schr\"odinger equation with oscillating coefficients