L p stability of solutions of Boltzmann equation with external force in soft potentials

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  • Chi Honn Cheng

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Original languageEnglish
Article number022007JMP
Journal / PublicationJournal of Mathematical Physics
Issue number7
Publication statusPublished - Jul 2010


In this paper, we present a uniform L p 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 L p norm of the distance between two mild solutions f and g, then define nonlinear functionals apply the Grönwall's inequality to obtain the L p stability. For large external forces, we make use of the constructive assumptions on external force, Minkowski's inequality Grönwall's inequality to derive the L p stability estimate. © 2010 American Institute of Physics.