On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $\mathbb{T}$
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916888457510912 |
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| author | McConnell, Ryan |
| author_facet | McConnell, Ryan |
| contents | We prove and utilize an improvement to the short time estimates of Burq, Gérard, & Tzvetkov on $\mathbb{T}$ via connecting this estimate to the number of lattice points in thin annuli. As a consequence, we enhance the well-posedness level of the periodic quintic Nonlinear Schrödinger equation to $s > \frac{131}{624}\sim 0.21$, which is an improvement on the results of De Silva, Pavlović, Staffilani, & Tzirakis, Li, Wu, & Xu, and Schippa. We also present conditional results, dependent on improvements on the count of lattice points in thin annuli. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_01638 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $\mathbb{T}$ McConnell, Ryan Analysis of PDEs We prove and utilize an improvement to the short time estimates of Burq, Gérard, & Tzvetkov on $\mathbb{T}$ via connecting this estimate to the number of lattice points in thin annuli. As a consequence, we enhance the well-posedness level of the periodic quintic Nonlinear Schrödinger equation to $s > \frac{131}{624}\sim 0.21$, which is an improvement on the results of De Silva, Pavlović, Staffilani, & Tzirakis, Li, Wu, & Xu, and Schippa. We also present conditional results, dependent on improvements on the count of lattice points in thin annuli. |
| title | On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on $\mathbb{T}$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.01638 |