Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions

Abstract

We consider a class of $L^2$-supercritical inhomogeneous nonlinear Schrödinger equations in two dimensions \[ i\partial_t u + Δu = \pm |x|^{-b} |u|^αu, \quad (t,x) \in \mathbb{R} \times \mathbb{R}^2, \] where $0<b<1$ and $\alpha >2-b$. By adapting a new approach of Arora-Dodson-Murphy \cite{ADM}, we show the energy scattering for the equation with radially symmetric initial data. In the focusing case, our result extends the one of Farah-Guzmán \cite{FG-high} to the whole range of $b$ where the local well-posedness is available. In the defocusing case, our result extends the one in \cite{Dinh-scat} where the energy scattering for non-radial initial data was established in dimensions $N\ge 3$.

arXiv comment17 pages, some typos are corrected