调和分析和偏微分方程研讨班：On the L2 rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation

中科院数学与系统科学研究院

数学研究所

学术报告

调和分析和偏微分方程研讨班

报告人：Jacky Chong (Peking University)

题  目：On the L² rate of convergence in the limit from the Hartree to the Vlasov–Poisson Equation

时  间：2023.04.04（星期二）16:00-17:00

地  点：数学院南楼N802

摘  要： We consider the semiclassical limit from the Hartree equation with Coulomb interaction potential to the Vlasov–Poisson equation. Using a new stability estimate for the difference of the square roots of two solutions of the Vlasov–Poisson equation, we obtain the convergence in the L² norm of the Wigner transform of a solution of the Hartree equation with Coulomb potential to a solution of the Vlasov–Poisson equation, with a rate of convergence proportional to ћ. This improves on the result of ћ^3/4−ε rate of convergence in L² obtained in [3]. If time permits, we shall discuss its connection to the derivation of Vlasov equation from many-body quantum dynamics given in [1]. The talk is based on our recent paper [2] with the same title. This is a joint work with Laurent Lafleche and Chiara Saffirio. The talk will be delivered in English.

References

[1] J. Chong, L. Lafleche, and C. Saffirio. From Many-Body Quantum Dynamics to theHartree–Fock and Vlasov Equations with Singular Potentials. arXiv:2103.10946, pages 1–74, Mar. 2021.

[2] J. Chong, L. Lafleche, and C. Saffirio. On the L² Rate of Convergence in the Limit from the Hartree to the Vlasov–Poisson Equation. Journal de l'Ecole polytechnique — Mathematiques, to appear:1–21, Apr. 2023.

[3] L. Lafleche and C. Saffirio. Strong Semiclassical Limit from Hartree and Hartree–Fock to Vlasov–Poisson Equation. Analysis & PDE, to appear:1–35, Oct. 2021.