Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915153747902464 |
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| author | Kato, Takamori |
| author_facet | Kato, Takamori |
| contents | We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\mathbb{T}) when s \geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus Kato, Takamori Analysis of PDEs We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\mathbb{T}) when s \geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses. |
| title | Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.11455 |