Logo image
Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions
Journal article   Open access   Peer reviewed

Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions

Dong Li and Xiaoyi Zhang
Journal of functional analysis, Vol.256(6), pp.1928-1961
2009
DOI: 10.1016/j.jfa.2008.12.007
url
https://doi.org/10.1016/j.jfa.2008.12.007View
Published (Version of record) Open Access

Abstract

In [T. Duyckaerts, F. Merle, Dynamic of threshold solutions for energy-critical NLS, preprint, arXiv:0710.5915 [math.AP]], T. Duyckaerts and F. Merle studied the variational structure near the ground state solution W of the energy critical NLS and classified the solutions with the threshold energy E ( W ) in dimensions d = 3 , 4 , 5 under the radial assumption. In this paper, we extend the results to all dimensions d ⩾ 6 . The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of W.
Energy critical Ground state Schrödinger equation Variational structure

Details

Metrics

Logo image