Kinetic maximal Lμp(Lp)-regularity for the fractional Kolmogorov equation with variable density. (January 2022)

• Record Type: Journal Article
• Authors: Niebel, Lukas
• Is Part Of: Nonlinear analysis. Volume 214(2022)
• Publication Date: 2022-01
• Subjects: 35K59, 35K65, 45K05; Kinetic maximal Lp-regularity -- Fractional Kolmogorov equation -- Non-local integro-differential kinetic equations -- Quasilinear kinetic equations; 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.2021.112517
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We consider the Kolmogorov equation, where the right-hand side is given by a non-local integro-differential operator comparable to the fractional Laplacian in velocity with possibly time, space and velocity dependent density. We prove that this equation admits kinetic maximal L μ p -regularity under suitable assumptions on the density and on p and μ . We apply this result to prove short-time existence of strong L μ p -solutions to quasilinear non-local kinetic partial differential equations.