Modified Scattering for Nonlocal Nonlinear Schrödinger Equations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909895289208832 |
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| author | Van Hoose, Tim |
| author_facet | Van Hoose, Tim |
| contents | We prove a modified scattering and sharp $L^\infty$ decay result for both the Hartree and Schrödinger-Bopp-Podolsky equations in dimensions $2$ and $3$ using the testing by wavepackets approach due to Ifrim and Tataru. We show that modified scattering and sharp pointwise decay occur for these equations at a regularity much lower than previous results due to Hayashi-Naumkin and Kato-Pusateri, and as a corollary also show that the results on power-type scattering-critical NLS due to Hayashi-Naumkin can be proven under minimal regularity assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06637 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modified Scattering for Nonlocal Nonlinear Schrödinger Equations Van Hoose, Tim Analysis of PDEs 35P25 (Primary) 35Q55 (Secondary) We prove a modified scattering and sharp $L^\infty$ decay result for both the Hartree and Schrödinger-Bopp-Podolsky equations in dimensions $2$ and $3$ using the testing by wavepackets approach due to Ifrim and Tataru. We show that modified scattering and sharp pointwise decay occur for these equations at a regularity much lower than previous results due to Hayashi-Naumkin and Kato-Pusateri, and as a corollary also show that the results on power-type scattering-critical NLS due to Hayashi-Naumkin can be proven under minimal regularity assumptions. |
| title | Modified Scattering for Nonlocal Nonlinear Schrödinger Equations |
| topic | Analysis of PDEs 35P25 (Primary) 35Q55 (Secondary) |
| url | https://arxiv.org/abs/2511.06637 |