A smoothing effect for the fractional Schrödinger equations on the circle and observability
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916618548805632 |
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| author | Alphonse, Paul Tzvetkov, Nikolay |
| author_facet | Alphonse, Paul Tzvetkov, Nikolay |
| contents | We show that, after a renormalisation, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A smoothing effect for the fractional Schrödinger equations on the circle and observability Alphonse, Paul Tzvetkov, Nikolay Analysis of PDEs We show that, after a renormalisation, 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. |
| title | A smoothing effect for the fractional Schrödinger equations on the circle and observability |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.12763 |