Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with radial initial data

Abstract

In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations. This system was introduced by M. Colin and T. Colin (2004). The first and second authors obtained some well-posedness results in the Sobolev space $H^s({\mathbb{R}}^d)$. We improve these results for conditional radial initial data by rewriting the system radial form.

28 pages. arXiv admin note: text overlap with arXiv:1802.06563