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

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 $s>1/4$.

35 pages. A shorter version of this article has been published in Adv. Contin. Discrete Models 2023, 10, https://doi.org/10.1186/s13662-023-03756-6