Quadratic Nonlinear Derivative Schrödiger Equations - Part 1

Abstract

In this paper we consider the local well-posedness theory for the quadratic nonlinear Schrödinger equation with low regularity initial data in the case when the nonlinearity contains derivatives. We work in 2+1 dimensions and prove a local well-posedness result up to the scaling for small initial data with some spherical symmetry structure.

References in corpus (2)

• Global regularity of wave maps II. Small energy in two dimensions
• On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations

Cited by in corpus (3)

• On Schrödinger Maps
• Local well-posedness for quadratic Schrödinger equations in ${\mathbf{R}}^{1+1}$: a normal form approach
• Global existence and uniqueness of Schrödinger maps in dimensions $d\ge 4$