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arXiv · 2606.00389

Strichartz Estimates and Small-Mass Global Well-Posedness for the Periodic Quintic NLS in 1D

Nikolaos Skouloudis·Jiahui Yu
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Abstract

We consider the periodic quintic nonlinear Schr\"odinger 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.

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Nikolaos Skouloudis, Jiahui Yu. 2026-05-29. Strichartz Estimates and Small-Mass Global Well-Posedness for the Periodic Quintic NLS in 1D. https://arxiv.org/abs/2606.00389

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