Strichartz Estimates and Small-Posedness Global Well-Posedness for the Periodic Quintic NLS in 1D
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914619628453888 |
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| author | Skouloudis, Nikolaos Yu, Jiahui |
| author_facet | Skouloudis, Nikolaos Yu, Jiahui |
| contents | We consider the periodic quintic nonlinear Schrödinger and prove small-mass global well-posedness in $H^s(\mathbb{T})$ for $s>0$. The proof relies on a new derivative-loss-free $L^6_{t,x}$ Strichartz estimate which is established using the high-low method, an asymmetric superlevel set estimate and a new refined broad-narrow argument. Although our $L^6_{t,x}$ Strichartz estimate is not sharp, being valid on slightly shorter time scales than the optimal logarithmic scale, combining it with the $I$-method enables the extension of local solutions to arbitrary times. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2606_00389 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strichartz Estimates and Small-Posedness Global Well-Posedness for the Periodic Quintic NLS in 1D Skouloudis, Nikolaos Yu, Jiahui Analysis of PDEs We consider the periodic quintic nonlinear Schrödinger and prove small-mass global well-posedness in $H^s(\mathbb{T})$ for $s>0$. The proof relies on a new derivative-loss-free $L^6_{t,x}$ Strichartz estimate which is established using the high-low method, an asymmetric superlevel set estimate and a new refined broad-narrow argument. Although our $L^6_{t,x}$ Strichartz estimate is not sharp, being valid on slightly shorter time scales than the optimal logarithmic scale, combining it with the $I$-method enables the extension of local solutions to arbitrary times. |
| title | Strichartz Estimates and Small-Posedness Global Well-Posedness for the Periodic Quintic NLS in 1D |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2606.00389 |