On the propagation of high regularity for the logarithmic Schrödinger equation

2025/05/16 by Chauleur, Quentin, Ferriere, Guillaume
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.10916

Abstract

We investigate both the instantaneous loss and the persistence of high regularity for the one-dimensional logarithmic Schrödinger equation in symmetric domains under various boundary conditions. We show that for a broad class of odd initial data, the H^s-norm of solutions exhibits instantaneous blow-up for all s > 7/2 . Conversely, we establish that H³-regularity is preserved for solutions that are odd with first-order cancellation, non-vanishing behavior away from the origin and Neumann boundary conditions on symmetric bounded domains. These theoretical results are further supported and illustrated by numerical simulations.

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