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arXiv · 2609.28454

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 $u_0\in L^2$, 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.

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Zuyu Ma, Changxing Miao, Matthew Rosenzweig, Jiqiang Zheng. 2026-09-23. Global well-posedness and scattering for mass-critical Hartree equation. https://arxiv.org/abs/2609.28454

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