MR3468736 Hiroyuki HIRAYAMA Hiroyuki HIRAYAMA Well-Posedness and Scattering for Nonlinear Schrödinger Equations with a Derivative Nonlinearity at the Scaling Critical Regularity Funkcialaj Ekvacioj. Serio Internacia 58 2015 431--450 http://fe.math.kobe-u.ac.jp/FE/FullPapers/58-3/58_431.pdf http://www.ams.org/mathscinet-getitem?mr=MR3468736 In the present paper, we consider the Cauchy problem of nonlinear Schrödinger equations with a derivative nonlinearity which depends only on $\overline{u}$. 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 $U^2$ space and $V^2$ 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). Schrödinger equation, Well-posedness, Cauchy problem, Scaling critical, Multilinear estimate, Bounded $p$-variation. 35Q55, 35B65. 58-431 2015 Well-Posedness and Scattering for Nonlinear Schrödinger Equations with a Derivative Nonlinearity at the Scaling Critical Regularity Hiroyuki HIRAYAMA Hiroyuki HIRAYAMA
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