On the propagation of high regularity for the logarithmic Schr{\"o}dinger equation

Quentin Chauleur; Guillaume Ferriere

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arXiv · 2505.10916

On the propagation of high regularity for the logarithmic Schr{\"o}dinger equation

Quentin Chauleur·Guillaume Ferriere

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Abstract

We investigate both the instantaneous loss and the persistence of high regularity for the one-dimensional logarithmic Schr{\"o}dinger 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 $H^3$-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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Quentin Chauleur, Guillaume Ferriere. 2025-05-16. On the propagation of high regularity for the logarithmic Schr{\"o}dinger equation. https://arxiv.org/abs/2505.10916

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