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arXiv · 2403.12763

A smoothing effect for the fractional Schr\"odinger equations on the circle and observability

Paul Alphonse·Nikolay Tzvetkov
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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.

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Paul Alphonse, Nikolay Tzvetkov. 2024-03-19. A smoothing effect for the fractional Schr\"odinger equations on the circle and observability. https://arxiv.org/abs/2403.12763

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