On local well-posedness for Hs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s$$\end{document}-critical nonlinear Schrödinger equations

This paper concerns the Cauchy problem for the nonlinear Schrödinger equation with power nonlinearity. Time local well-posedness in Hs(RN)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s(\mathbb {R}^N)$$\end{document} is proved in the case where the nonlinear term is critical from the scaling point of view, and has limited regularity so that the nonlinear term does not belong to Cs(R2;R2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^s(\mathbb {R}^2;\mathbb {R}^2)$$\end{document}.