Local decay estimates for the bi-Laplacian Nonautonomous Schrödinger equation
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908915737821184 |
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| author | Wu, Jiayan Zhang, Ting Zhou, Ruze |
| author_facet | Wu, Jiayan Zhang, Ting Zhou, Ruze |
| contents | In this paper, we establish local decay estimates for the bi-Laplacian Schrödinger equation with time-dependent (in particular, quasi-periodic) potentials in spatial dimension $n\ge14$. Moreover, under stronger spectral regularity hypotheses, the same result can be extended to dimension $n\ge9$. Our approach, based on asymptotic completeness and the existence of the channel wave operator, departs from standard resolvent-based methods. In addition, global-in-time Strichartz estimates are derived from the local decay estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25553 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Local decay estimates for the bi-Laplacian Nonautonomous Schrödinger equation Wu, Jiayan Zhang, Ting Zhou, Ruze Analysis of PDEs 35Q41, 35B40 In this paper, we establish local decay estimates for the bi-Laplacian Schrödinger equation with time-dependent (in particular, quasi-periodic) potentials in spatial dimension $n\ge14$. Moreover, under stronger spectral regularity hypotheses, the same result can be extended to dimension $n\ge9$. Our approach, based on asymptotic completeness and the existence of the channel wave operator, departs from standard resolvent-based methods. In addition, global-in-time Strichartz estimates are derived from the local decay estimates. |
| title | Local decay estimates for the bi-Laplacian Nonautonomous Schrödinger equation |
| topic | Analysis of PDEs 35Q41, 35B40 |
| url | https://arxiv.org/abs/2603.25553 |