{"title":"Global semiclassical limit from Hartree to Vlasov equation for concentrated initial data","authors":"Laurent Lafleche","doi":"10.1016/j.anihpc.2021.01.004","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a quantitative and <strong>global in time</strong><span> semiclassical limit from the Hartree to the Vlasov equation in the case of a singular interaction potential in dimension </span><span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span>, including the case of a Coulomb singularity in dimension <span><math><mi>d</mi><mo>=</mo><mn>3</mn></math></span><span>. This result holds for initial data<span> 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<span> of the spatial density due to dispersion effects, uniform in the Planck constant </span></span></span><em>ħ</em>.</p></div>","PeriodicalId":55514,"journal":{"name":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","volume":"38 6","pages":"Pages 1739-1762"},"PeriodicalIF":1.8000,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.anihpc.2021.01.004","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales De L Institut Henri Poincare-Analyse Non Lineaire","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S029414492100024X","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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 , including the case of a Coulomb singularity in dimension . 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.
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.