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PreprintCC BY 4.0arXiv

Global well-posedness and scattering for mass-critical Hartree equation

  • Zuyu Ma
  • Changxing Miao
  • Matthew Rosenzweig
  • Jiqiang Zheng
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Abstract

In this paper, we prove that the defocusing mass-critical Hartree equation is global well-posed and scatters for any initial data u0∈ L2, and prove the analogous result in the focusing case, provided the mass of u0 is strictly less than that of the ground state Q. This result removes the radial restriction from [C. Miao, G. Xu and L. Zhao, J. Math. Pures Appl. (9), 91(2009), 49-79.], thereby proving the scattering conjecture for the Hartree equation at the scaling-critical regularity.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026global,
  title = {{Global well-posedness and scattering for mass-critical Hartree equation}},
  author = {Zuyu Ma and Changxing Miao and Matthew Rosenzweig and Jiqiang Zheng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.28454},
  eprint = {2609.28454},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.28454},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Global well-posedness and scattering for mass-critical Hartree equation
AU  - Zuyu Ma
AU  - Changxing Miao
AU  - Matthew Rosenzweig
AU  - Jiqiang Zheng
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.28454
UR  - https://arxiv.org/abs/2609.28454
AB  - In this paper, we prove that the defocusing mass-critical Hartree equation is global well-posed and scatters for any initial data u_0∈ L^2, and prove the analogous result in the focusing case, provided the mass of u_0 is strictly less than that of the ground state Q. This result removes the radial restriction from [C. Miao, G. Xu and L. Zhao, J. Math. Pures Appl. (9), 91(2009), 49-79.], thereby proving the scattering conjecture for the Hartree equation at the scaling-critical regularity.
ER  -