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

Abstract

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

33 pages. arXiv admin note: text overlap with arXiv:1802.06563, arXiv:1811.08324

References in corpus (1)

• On the 2d Zakharov system with L^2 Schrödinger data

Cited by in corpus (1)

• Well-posedness and ill-posedness for a system of periodic quadratic derivative nonlinear Schrödinger equations