Uncertainty principle and kinetic equations
type: Item
instance of: scholarly article
title: Uncertainty principle and kinetic equations
zbMATH Open document ID: 1166.35038
author: Radjesvarane Alexandre
author: Yoshinori Morimoto
author: Seiji Ukai
author: Chao-Jiang Xu
author: Tong Yang
published in: Journal of Functional Analysis
publication date: 2008-12-22T00:00:00Z
review text: The main aim of the paper is to apply uncertainty principle to the study of smoothing effects arising from the non-cutoff cross-sections for the space inhomogeneous kinematic equations. Generalized version of the uncertainty principle is proved. Based on this version results on the smoothing effect on solutions to the kinematic equations are proved, by analyzing the interaction between the transport operator and the regularity assumption in the microscopic velocity, together with a mild regularity assumption on the source term. First the regularity for transport equation is regarded, then existence and regularity of solutions for linearized Boltzmann equation and linearized Landau equation are proved. Moreover, the regularity result for nonlinear Boltzmann equation is also proved.
reviewed by: Leszek Skrzypczak
Mathematics Subject Classification ID: 35S05
Mathematics Subject Classification ID: 76P05
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 35Q35
zbMATH DE Number: 5480725
zbMATH Keywords: uncertainty principle
zbMATH Keywords: kinematic equations
zbMATH Keywords: Boltzmann equation
zbMATH Keywords: Landau equation
MaRDI profile type: Publication
full work available at URL: j.jfa.2008.07.004
OpenAlex ID: W1966954380
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DOI: 10.1016/J.JFA.2008.07.004
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description: scientific article; zbMATH DE number 5480725