STRONG SEMICLASSICAL LIMITS FROM HARTREE AND HARTREE-FOCK TO VLASOV-POISSON EQUATIONS

被引：7

作者：

Lafleche, Laurent ^{[1
]}

Saffirio, Chiara ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Basel, Dept Math & Comp Sci, Basel, Switzerland

来源：

ANALYSIS & PDE | 2023年 / 16卷 / 04期

基金：

瑞士国家科学基金会;

关键词：

Hartree equation; Hartree-Fock equation; Vlasov equation; Coulomb interaction; gravitational interaction; semiclassical limit; MEAN-FIELD LIMIT; SCHRODINGER-EQUATION; PROPAGATION; SYSTEM; DERIVATION; UNIQUENESS; MOMENTS; CONVERGENCE; REGULARITY; EXISTENCE;

D O I：

10.2140/apde.2023.16.891

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the semiclassical limit from the Hartree to the Vlasov equation with general singular interaction potential including the Coulomb and gravitational interactions, and we prove explicit bounds in the strong topologies of Schatten norms. Moreover, in the case of fermions, we provide estimates on the size of the exchange term in the Hartree-Fock equation and also obtain a rate of convergence for the semiclassical limit from the Hartree-Fock to the Vlasov equation in Schatten norms. Our results hold for general initial data in some Sobolev space and any fixed time interval.

引用

页码：891 / 926

页数：40

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