Well-posedness for a system of quadratic derivative nonlinear Schrodinger equations in almost critical spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:499

Article

Hirayama, Hiroyuki¹  Kinoshita, Shinya²  Okamoto, Mamoru³ 

[1] Univ Miyazaki, Fac Educ, 1-1 Gakuenkibanadai Nishi, Miyazaki 8892192, Japan

[2] Univ Bielefeld, Fak Math, Postfach 10 01 31, D-33501 Bielefeld, Germany

[3] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

关键词: Schrodinger equation;    Well-posedness;    Cauchy problem;    Bilinear estimate;   

DOI  :  10.1016/j.jmaa.2021.125028

来源: Elsevier

【 摘 要 】

In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrodinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the Cauchy problem exists, except for the scaling critical case. This result covers a gap left open in papers of the first and second authors (2014, 2019). (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free