A remark on the well-posedness for a system of quadratic derivative nonlinear Schrödinger equations

Abstract

<p style='text-indent:20px;'>We consider the Cauchy problem for the system of quadratic derivative nonlinear Schrödinger equations, which was introduced by Colin and Colin (2004). In the previous paper, the authors (2021) determined the almost optimal Sobolev regularity to be well-posed in <inline-formula><tex-math id="M1">\begin{document}$ H^s ( \mathbb{R}^d) $\end{document}</tex-math></inline-formula> as long as we use the iteration argument. In this paper, we consider the well-posedness under the conditions where the flow map fails to be twice differentiable. To prove the well-posedness, we construct a modified energy and apply the energy method.</p>