Improved global well-posedness for mass-critical nonlinear Schrödinger equations on tori

2023/12/27 by Robert Schippa, Schippa, Robert · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2312.16527

openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show new global well-posedness results for mass-critical nonlinear Schrödinger equations on tori in one and two dimensions. For the quintic nonlinear Schrödinger equation on the circle we show global well-posedness for initial data in H^s(\mathbbT) for s>(1)/(3) and ‖ u₀ ‖_L²(\mathbbT) ≪ 1. In two dimensions we show global well-posedness on possibly irrational tori for s>(3)/(5). In the focusing case we need a smallness condition for the mass, whereas in the defocusing case large mass is covered.

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