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Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation
Abstract
Unconditional global existence and scattering are established for the three-dimensional focusing energy-critical generalized Hartree equation with 0<α<3, below the ground-state energy and kinetic thresholds. The initial data lie in Ḣ1, with no radial symmetry, finite-mass, or finite-variance assumption. Annular frequency estimates and Gaussian interaction estimates rule out a compact critical trajectory by first controlling its nonlinear forcing and then recovering its conserved mass.
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BibTeX
@misc{chung2026unconditional,
title = {{Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation}},
author = {Pang-hung Chung and Dan Han},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35700},
eprint = {2610.35700},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35700},
}
RIS
TY - UNPB
TI - Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation
AU - Pang-hung Chung
AU - Dan Han
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35700
UR - https://arxiv.org/abs/2610.35700
AB - Unconditional global existence and scattering are established for the three-dimensional focusing energy-critical generalized Hartree equation with 0<α<3, below the ground-state energy and kinetic thresholds. The initial data lie in Ḣ^1, with no radial symmetry, finite-mass, or finite-variance assumption. Annular frequency estimates and Gaussian interaction estimates rule out a compact critical trajectory by first controlling its nonlinear forcing and then recovering its conserved mass.
ER -