Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method

2023/03/30 by Nobu Kishimoto, Yoshio Tsutsumi, Kishimoto, Nobu +1 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2303.17360

openalex publication_date 2023/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces H^s with s>1/4.

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