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).

arXiv comment33 pages. arXiv admin note: text overlap with arXiv:1802.06563, arXiv:1811.08324

References in corpus (5)

• On the 2d Zakharov system with L^2 Schrödinger data
• A convolution estimate for two-dimensional hypersurfaces
• Well-posedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data
• Null structure in a system of quadratic derivative nonlinear Schrödinger equations
• Sharp bilinear estimates and its application to a system of quadratic derivative nonlinear Schrödinger equations

Cited by in corpus (1)

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