A smoothing effect for the fractional Schr\"odinger equations on the circle and observability
Analysis of PDEs
2025-02-19 v2
Abstract
We show that, after a renormalisation, one can define the square of the modulus of the solution of the fractional Schr\"odinger equations on the circle with data in Sobolev spaces of arbitrary negative index. As an application, we obtain observability estimates with rough controls.
Keywords
Cite
@article{arxiv.2403.12763,
title = {A smoothing effect for the fractional Schr\"odinger equations on the circle and observability},
author = {Paul Alphonse and Nikolay Tzvetkov},
journal= {arXiv preprint arXiv:2403.12763},
year = {2025}
}