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Dynamics for the energy critical nonlinear Schr\"odinger equation in high dimensions

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Type
Preprint
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Submission Date
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arXiv ID: 0902.0807
Source
arXiv
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Abstract

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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