A Smoothing Effect for the Fractional Schrödinger Equations on the Circle and Observability
Abstract We show that, after a renormalization, one can define the square of the modulus of the solution of the fractional Schrödinger equations on the circle with data in Sobolev spaces of arbitrary negative index. As an application, we obtain observability estimates with rough controls.
Authors
- Nikolay Tzvetkov (ORCID: https://orcid.org/0000-0002-8482-0481)
- Paul Alphonse (ORCID: https://orcid.org/0000-0003-0920-8943)
Institutions
- École Normale Supérieure de Lyon (FR)
- Centre National de la Recherche Scientifique (FR)
- Unité de Mathématiques Pures et Appliquées (FR)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-04-01
- DOI
- https://doi.org/10.1093/imrn/rnaf100
- Primary Topic
- Advanced Mathematical Physics Problems
- Type
- article
- Field-Weighted Citation Impact
- 0.00