Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus

2025/01/20 by Takamori Kato, Kato, Takamori
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2501.11455

openalex publication_date 2025/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\mathbbT) when s ≥ 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses.

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