Authors: Cazenave, Thierry; Correia, Simão; Dickstein, Flavio; Weissler, Fred B.

Venue: São Paulo Journal of Mathematical Sciences

Type: Publication

Abstract: In this paper we consider the nonlinear Schr��\-din\-ger equation $i u_t +��u +��|u|^��u=0$. We prove that if $��\frac {2} {N}$ and $��\in {\mathbb C}$, we improve the existing low energy scattering results in dimensions $N\ge 7$. More precisely, we prove that if $ \frac {8} {N + \sqrt{ N^2 +16N }} < ��\le \frac {4} {N} $, then small data give rise to global, scattering solutions in $H^1$.

DOI: 10.48550/arxiv.1506.00294