Boltzmann to Landau from the gradient flow perspective. (June 2022)

• Record Type: Journal Article
• Authors: Carrillo, José A.; Delgadino, Matias G.; Wu, Jeremy
• Is Part Of: Nonlinear analysis. Volume 219(2022)
• Publication Date: 2022-06
• Subjects: Boltzmann equation -- Plasma particles -- Kinetic theory -- Γ-convergence -- Gradient flows; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112824
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker–Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the Γ -convergence of gradient flows technique introduced by Sandier and Serfaty [39] ; Serfaty [41] . In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation.