Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions

Details Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions Dynamics for the energy critical nonlinear Schrödinger equation in high dimensions

2009-02-04

arxiv.org/abs/0902.0807v1

Mathematics

Analysis of PDEs

30 Pages. To appear JFA

Scientific paper

In \cite{duck-merle}, 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 $d\ge 6$. 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 $W$.

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