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Multisoliton solutions and blow up for the $L^2$-critical...
[Submitted on 30 Jan 2025 (v1), last revised 25 Jun 2026 (this v · 2026-06-26 · via math updates on arXiv.org

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Abstract:We construct multisoliton solutions for the $L^2$-critical Hartree equation with trajectories asymptotically obeying a many-body law for an inverse square potential. Precisely, we consider the $m$-body hyperbolic and parabolic non-trapped dynamics. The pseudo-conformal symmetry then implies finite-time collision blow up in the latter case and a solution blowing up at $m$ distinct points in the former case. The approach we take is based on the ideas of [Krieger-Martel-Raphaël, 2009] and the third author's recent extension [Wu, 2026]. The approximation scheme requires new aspects in order to deal with a certain degeneracy for generalized root space elements.

Submission history

From: Yutong Wu [view email]
[v1] Thu, 30 Jan 2025 14:54:56 UTC (40 KB)
[v2] Thu, 25 Jun 2026 17:54:17 UTC (44 KB)