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arXiv · 1811.07239

Dynamics of subcritical threshold solutions for energy-critical NLS

Qingtang Su·Zehua Zhao
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Abstract

In this paper, we study the dynamics of subcritical threshold solutions for focusing energy critical NLS on $\mathbb{R}^d$ ($d\geq 5$) with nonradial data. This problem with radial assumption was studied by T. Duyckaerts and F. Merle in \cite{DM} for $d=3,4,5$ and later by D. Li and X. Zhang in \cite{LZ} for $d \geq 6$. We generalize the conclusion for the subcritical threshold solutions by removing the radial assumption for $d\geq 5$. A key step is to show exponential convergence to the ground state $W(x)$ up to symmetries if the scattering phenomenon does not occur. Remarkably, an interaction Morawetz-type estimate are applied.

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Qingtang Su, Zehua Zhao. 2018-11-17. Dynamics of subcritical threshold solutions for energy-critical NLS. https://arxiv.org/abs/1811.07239

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