Propagation of Regularity for Schroedinger Equations with Time Dependent Potentials
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917546546954240 |
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| author | Soffer, Avy |
| author_facet | Soffer, Avy |
| contents | The dynamics of Schrödinger equation with time dependent potentials of general time dependence is considered. It is shown that for localized in space potentials, there is propagation of regularity which is uniformly bounded in higher Sobolev norms. Unlike the cases where the solution scatter, and then propagation is proved via a standard bootstrap argument, the solutions considered here have a part that does not scatter, as expected in general. For this we introduce propagation estimates that work directly in (e.g.) $H^2(\mathcal{R}^3).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27321 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Propagation of Regularity for Schroedinger Equations with Time Dependent Potentials Soffer, Avy Analysis of PDEs 35Bxx The dynamics of Schrödinger equation with time dependent potentials of general time dependence is considered. It is shown that for localized in space potentials, there is propagation of regularity which is uniformly bounded in higher Sobolev norms. Unlike the cases where the solution scatter, and then propagation is proved via a standard bootstrap argument, the solutions considered here have a part that does not scatter, as expected in general. For this we introduce propagation estimates that work directly in (e.g.) $H^2(\mathcal{R}^3).$ |
| title | Propagation of Regularity for Schroedinger Equations with Time Dependent Potentials |
| topic | Analysis of PDEs 35Bxx |
| url | https://arxiv.org/abs/2605.27321 |