On 2D Scattering for a Critical Nonlinear Schrödinger Flow

Abstract

We study modified scattering for the two-dimensional defocusing nonlinear Schrödinger equation (NLS) with the gauge-invariant, scattering-critical nonlinearity $|u|u$. We prove that the remodulated interaction representation has a local $L^2$ limit for general data in $Σ=H^1\cap\F^{-1}H^1$. For radial data, we prove convergence in $L^p({\mathbb{R}}^2)$ for every $2<p<\infty$.