Nonlinear stability of rarefaction waves for the Boltzmann equation

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • Tai-Ping LIU
  • Tong YANG
  • Shih-Hsien YU
  • Hui-Jiang ZHAO

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)333-371
Journal / PublicationArchive for Rational Mechanics and Analysis
Volume181
Issue number2
Online published27 Jan 2006
Publication statusPublished - Jul 2006

Abstract

It is well known that the Boltzmann equation is related to the Euler and Navier-Stokes equations in the field of gas dynamics. The relation is either for small Knudsen number, or, for dissipative waves in the time-asymptotic sense. In this paper, we show that rarefaction waves for the Boltzmann equation are time-asymptotic stable and tend to the rarefaction waves for the Euler and Navier-Stokes equations. Our main tool is the combination of techniques for viscous conservation laws and the energy method based on micro-macro decomposition of the Boltzmann equation. The expansion nature of the rarefaction waves and the suitable microscopic version of the H-theorem are essential elements of our analysis.

Citation Format(s)

Nonlinear stability of rarefaction waves for the Boltzmann equation. / LIU, Tai-Ping; YANG, Tong; YU, Shih-Hsien et al.
In: Archive for Rational Mechanics and Analysis, Vol. 181, No. 2, 07.2006, p. 333-371.

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review