Well-Posedness and Scattering for Nonlinear Schrödinger Equations with a Derivative Nonlinearity at the Scaling Critical Regularity

抄録

In the present paper, we consider the Cauchy problem of nonlinear Schrödinger equations with a derivative nonlinearity which depends only on ū and its first derivatives. The well-posedness of the equation at the scaling subcritical regularity was proved by A. Grünrock (2000). We prove the well-posedness of the equation and the scattering for the solution at the scaling critical regularity by using U² space and V² space which are applied to prove the well-posedness and the scattering for KP-II equation at the scaling critical regularity by Hadac, Herr and Koch (2009).