Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data

IF 1.8 1区 数学 Q1 MATHEMATICS, APPLIED
Laurent Lafleche
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引用次数: 17

Abstract

We prove a quantitative and global in time semiclassical limit from the Hartree to the Vlasov equation in the case of a singular interaction potential in dimension d3, including the case of a Coulomb singularity in dimension d=3. This result holds for initial data concentrated enough in the sense that some space moments are initially sufficiently small. As an intermediate result, we also obtain quantitative bounds on the space and velocity moments of even order and the asymptotic behavior of the spatial density due to dispersion effects, uniform in the Planck constant ħ.

集中初始数据从Hartree到Vlasov方程的全局半经典极限
我们证明了d≥3维的奇异相互作用势,包括d=3维的库仑奇点的情况下,从Hartree到Vlasov方程的一个定量的、全局的时间半经典极限。这个结果适用于初始数据足够集中的情况,因为某些空间矩最初足够小。作为一个中间结果,我们还得到了偶数阶空间和速度矩的定量界限,以及由于色散效应而导致的空间密度的渐近行为,在普朗克常数中是均匀的。
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来源期刊
CiteScore
4.10
自引率
5.30%
发文量
62
审稿时长
>12 weeks
期刊介绍: The Nonlinear Analysis section of the Annales de l''Institut Henri Poincaré is an international journal created in 1983 which publishes original and high quality research articles. It concentrates on all domains concerned with nonlinear analysis, specially applicable to PDE, mechanics, physics, economy, without overlooking the numerical aspects.
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