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PreprintCC0arXiv

Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the L2-critical level

  • Zuyu Ma
  • Changxing Miao
  • Jiqiang Zheng
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Abstract

In this paper, we study the focusing mass-critical Hartree equation iut+Δu=−(|x|−2*|u|2)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 L2 and removes the radial assumption in the global case.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026classification,
  title = {{Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the $L^2$-critical level}},
  author = {Zuyu Ma and Changxing Miao and Jiqiang Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.15460},
  eprint = {2610.15460},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.15460},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the L^2-critical level
AU  - Zuyu Ma
AU  - Changxing Miao
AU  - Jiqiang Zheng
PY  - 2026
DA  - 2026/10/11
PB  - arXiv
DO  - 10.48550/arxiv.2610.15460
UR  - https://arxiv.org/abs/2610.15460
AB  - In this paper, we study the focusing mass-critical Hartree equation iu_t+Δu=−(|x|^−2*|u|^2)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.
ER  -