Mathematics > Analysis of PDEs
[Submitted on 4 Aug 2025
]
Title: Dynamics of subcritical threshold solutions for the 4d energy-critical NLS
Title: 4维能量临界NLS的次临界阈值解的动力学
Abstract: We study dynamics of the 4$d$ energy-critical nonlinear Schr\"odinger equation at the ground state energy. Previously, Duyckaerts and Merle [Geom. Funct. Anal. (2009)] proved that any radial solution with kinetic energy less than that of the ground state either scatters in both time directions or coincides (modulo symmetries) with a heteroclinic orbit, which scatters in one time direction and converges to the ground state in the other. We extend this result to the non-radial setting.
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