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arXiv · 2303.17360

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

Nobu Kishimoto·Yoshio Tsutsumi
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Abstract

In this article, we consider the kinetic derivative nonlinear Schr\"odinger equation (KDNLS), which is a one-dimensional nonlinear Schr\"odinger 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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Nobu Kishimoto, Yoshio Tsutsumi. 2023-03-30. Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method. https://arxiv.org/abs/2303.17360

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