L1 and BV-type stability of the Boltzmann equation with external forces

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1-28
Journal / PublicationJournal of Differential Equations
Volume227
Issue number1
Publication statusPublished - 1 Aug 2006

Abstract

Based on the existence theory on the Boltzmann equation with external forces in infinite vacuum, in this paper, we will study the L1 and BV-type stability of the classical solutions for small initial data. The stability results generalize those for the Boltzmann equation without force to the case with external force. In particular, we show that the stability can be established for the soft potentials directly, while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals. The functionals thus constructed generalize those constructed in [S.-Y. Ha, Nonlinear functionals of the Boltzmann equation and uniform stability estimates, J. Differential Equations 215 (2005) 178-205] for the case without force to capture the effect of the force term on the time evolution of the solutions. © 2006 Elsevier Inc. All rights reserved.

Research Area(s)

  • Bi-characteristics, Boltzmann equation, Lyapunov functional, Stability

Citation Format(s)

L1 and BV-type stability of the Boltzmann equation with external forces. / Duan, Renjun; Yang, Tong; Zhu, Changjiang.
In: Journal of Differential Equations, Vol. 227, No. 1, 01.08.2006, p. 1-28.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review