On soliton clusters and collision blow up for the $L^2$-critical Hartree equation

Tobias Schmid; Yutong Wu

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arXiv · 2606.30640

On soliton clusters and collision blow up for the $L^2$-critical Hartree equation

Tobias Schmid·Yutong Wu

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Abstract

We consider the $L^2$-critical nonlinear Hartree equation in $\mathbb{R}^{1+4}$ and multisoliton solutions for which the trajectories are approximated to leading order by an $m$-body law. We obtain soliton clusters asymptotically following hyperbolic-parabolic trajectories of the corresponding $m$-body problem. By pseudo-conformal invariance, we then conclude finite-time collision blow-up with any number of clusters, each consisting of an arbitrary number of solitons, colliding simultaneously at distinct prescribed points.

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Tobias Schmid, Yutong Wu. 2026-06-29. On soliton clusters and collision blow up for the $L^2$-critical Hartree equation. https://arxiv.org/abs/2606.30640

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