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arXiv · 2610.15460

Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the $L^2$-critical level

Zuyu Ma·Changxing Miao·Jiqiang Zheng
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Abstract

In this paper, we study the focusing mass-critical Hartree equation \[ iu_t+Δu=-\bigl(|x|^{-2}*|u|^2\bigr)u \] at the ground-state mass $M(Q)$. We prove that, up to the symmetries of the equation, every global minimal-mass non-scattering solution is a solitary wave, while every finite-time minimal-mass blowup solution is a pseudo-conformal image of a solitary wave. This extends the results of \cite{LZ28,Miao-Xu-Zhao3,Wang-Gao} to the scaling-critical space $L^2$ and removes the radial assumption in the global case.

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Zuyu Ma, Changxing Miao, Jiqiang Zheng. 2026-10-11. Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the $L^2$-critical level. https://arxiv.org/abs/2610.15460

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