On Lattice Points, Short-Time Estimates, and Global Well-posedness of the Quintic NLS on \mathbbT

2023/10/02 by Ryan McConnell, McConnell, Ryan
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2310.01638

openalex publication_date 2023/10/02 · openalex created_date 2023/10/05 · openalex updated_date 2026/07/28

Abstract

We prove and utilize an improvement to the short time estimates of Burq, Gérard, & Tzvetkov on \mathbbT 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 > (131)/(624)∼ 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.

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