Pointwise Convergence of the Schrödinger Flow

E. Compaan, R. Lucà, G. Staffilani

Published 2019-07-25Version 1

In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flow to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing effects for the non-homogeneous part of the solution can be used to upgrade to an everywhere convergence to zero of that part and we discuss the sharpness of the results obtained. We also use randomization techniques to prove almost everywhere convergence with much less regularity of the initial data, hence showing how more generic results can be obtained.