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Global well-posedness for the energy-critical focusing NLS on đť•‹3
Abstract
We prove global well-posedness for the focusing quintic nonlinear Schrödinger equation on the standard three-dimensional torus for initial data below the mass-corrected energy and Sobolev-norm thresholds determined by the Euclidean ground state. This gives a subthreshold focusing counterpart to the defocusing theorem of Ionescu and Pausader. The proof combines the periodic profile analysis with the recent nonradial Euclidean scattering theorem of Su and Zhao. The mass correction yields an invariant region and a nonnegative energy decomposition, placing every Euclidean profile below both ground-state thresholds. Uniform bounds on finite intervals follow from a contradiction argument on shrinking time intervals.
Related
- Global well-posedness and scattering of energy-critical defocusing nonlinear Schrödinger equation on high-dimensional hyperbolic spaces
- Global well-posedness of the energy-critical nonlinear Schrödinger equation on the three-dimensional torus with additive Lévy noise
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BibTeX
@misc{chen2026global,
title = {{Global well-posedness for the energy-critical focusing NLS on $\mathbb T^3$}},
author = {Meng Chen and Han Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07740},
eprint = {2611.07740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07740},
}
RIS
TY - UNPB
TI - Global well-posedness for the energy-critical focusing NLS on đť•‹^3
AU - Meng Chen
AU - Han Wang
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07740
UR - https://arxiv.org/abs/2611.07740
AB - We prove global well-posedness for the focusing quintic nonlinear Schrödinger equation on the standard three-dimensional torus for initial data below the mass-corrected energy and Sobolev-norm thresholds determined by the Euclidean ground state. This gives a subthreshold focusing counterpart to the defocusing theorem of Ionescu and Pausader. The proof combines the periodic profile analysis with the recent nonradial Euclidean scattering theorem of Su and Zhao. The mass correction yields an invariant region and a nonnegative energy decomposition, placing every Euclidean profile below both ground-state thresholds. Uniform bounds on finite intervals follow from a contradiction argument on shrinking time intervals.
ER -