Work

A Smoothing Effect for the Fractional Schrödinger Equations on the Circle and Observability

Year: 2025

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf100

Authors: Paul Alphonse, Nikolay Tzvetkov

Institutions: École Normale Supérieure de Lyon, Centre National de la Recherche Scientifique, Unité de Mathématiques Pures et Appliquées

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: Smooth Calculus for Low Regularity Random Data Partial Differential Equations