质量临界 Hartree 方程的全局适定性与散射
Global well-posedness and scattering for mass-critical Hartree equation
- Graduate School of China Academy of Engineering Physics（中国工程物理研究院研究生部）
- School of Mathematics and Physics, University of Science and Technology Beijing（北京科技大学数理学院）
- Department of Mathematical Sciences, Carnegie Mellon University（卡内基梅隆大学数学系）
- Institute of Applied Physics and Computational Mathematics and National Key Laboratory of Computational Physics（应用物理与计算数学研究所及计算物理学国家重点实验室）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在标度临界正则性下证明了质量临界 Hartree 方程的散射猜想，去除了径向限制，涵盖散焦与聚焦（质量小于基态）情形。
AI中文摘要：
本文证明了散焦质量临界 Hartree 方程对任意初始数据 $u_0\in L^2$ 是全局适定的且散射，并证明了聚焦情形下的类似结果，前提是 $u_0$ 的质量严格小于基态 $Q$ 的质量。该结果去除了 [C. Miao, G. Xu and L. Zhao, J. Math. Pures Appl. (9), 91(2009), 49-79.] 中的径向限制，从而在标度临界正则性下证明了 Hartree 方程的散射猜想。
英文摘要：
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.
