Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation

Pang-hung Chung; Dan Han

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arXiv · 2610.35700

Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation

Pang-hung Chung·Dan Han

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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 $\dot H^1$, 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.

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Pang-hung Chung, Dan Han. 2026-10-26. Unconditional scattering below the ground state for the three-dimensional focusing energy-critical generalized Hartree equation. https://arxiv.org/abs/2610.35700

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