Lp stability of solutions of Boltzmann equation with external force in soft potentials

Autor:	Chi Honn Cheng
Rok vydání:	2010
Předmět:	Nonlinear system Partial differential equation Stability theory Time derivative Minkowski space Mathematical analysis Statistical and Nonlinear Physics Space (mathematics) Lp space Boltzmann equation Mathematical Physics Mathematics
Zdroj:	Journal of Mathematical Physics. 51:073303
ISSN:	1089-7658 0022-2488
DOI:	10.1063/1.3459940
Popis:	In this paper, we present a uniform Lp stability theory for the solutions to Boltzmann equation with small or large external forces in vacuum in soft potentials. We assume that the initial data are sufficiently small and a fast decay in space and velocity. Our stability analysis is divided into two parts. For small external forces, we first consider the time derivative of the pth power of Lp norm of the distance between two mild solutions f and g, then define nonlinear functionals, and apply the Gronwall’s inequality to obtain the Lp stability. For large external forces, we make use of the constructive assumptions on external force, Minkowski’s inequality, and Gronwall’s inequality to derive the Lp stability estimate.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2a86a284d530b3ee7a3e37e187734385 https://doi.org/10.1063/1.3459940 Zobrazit plný text záznamu