Local smoothing with a prescribed loss for the Schrodinger equation

Hans Christianson (North Carolina)

Abstract: Local smoothing estimates express that, on average in time and locally in space, solutions to the Schrodinger equation are more regular than the initial data. It is known that the presence of trapped geodesics forces a loss in the local smoothing effect, but not too many examples have been studied. In this work (joint with J. Wunsch), we study some examples which fill in the gap between no loss and total loss in the smoothing effect.