Global well-posedness for the defocusing cubic nonlinear Schrödinger equation on \Bbb T³

2024/11/15 by Yilin Song, Song, Yilin, Ruixiao Zhang +1
Mathematics · #35Q55 #35R01 #37K06 #37L50 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2411.10056

openalex publication_date 2024/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we investigate the global well-posedness for the defocusing, cubic nonlinear Schrödinger equation posed on \T³ with intial data lying in its critical space H^(1)/(2)(\T³). By establishing the linear profile decomposition, and applied this to the concentration-compactness/rigidity argument, we prove that if the solution remains bounded in the critical Sobolev space throughout the maximal lifespan, i.e. u∈ L_t^∞H^(1)/(2)(I×\T³), then u is global.

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