Well-posedness and scattering for nonlinear Schrödinger equations with a derivative nonlinearity at the scaling critical regularity

Abstract

In the present paper, we consider the Cauchy problem of nonlinear Schrödinger equations with a derivative nonlinearity which depends only on $\bar{u}$. 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).

19 pages. arXiv admin note: substantial text overlap with arXiv:1309.4336

Cited by in corpus (4)

• Random data Cauchy problem for the nonlinear Schrödinger equation with derivative nonlinearity
• Small data well-posedness for derivative nonlinear Schrödinger equations
• Well-posedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity
• Optimal small data Scattering for the generalized derivative nonlinear Schrödinger equations