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

Nobu Kishimoto; Yoshio Tsutsumi

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

Analysis of PDEs 2023-03-31 v1

Authors: Nobu Kishimoto , Yoshio Tsutsumi

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 $s>1/4$ .

Keywords

kinetic derivative nonlinear Schrödinger equation a priori estimate short-time Fourier restriction low regularity Cauchy problem Sobolev space

Cite

@article{arxiv.2303.17360,
  title  = {Low regularity a priori estimate for KDNLS via the short-time Fourier restriction method},
  author = {Nobu Kishimoto and Yoshio Tsutsumi},
  journal= {arXiv preprint arXiv:2303.17360},
  year   = {2023}
}

Comments

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

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