Asymptotic Expansions of Solutions for the Boltzmann Equation

Russel E. Caflisch

Research output: Contribution to journalArticle


The Hilbert and Chapman-Enskog expansions approximate solutions of the Boltzmann equation, but each has some disadvantages: The Hilbert expansion, which results in nonlinear and linearized Euler equations, is invalid for weak shocks, weak boundary layers and long time asymptotics. The Chapman-Enskog expansion results in nonlinear Euler then Navier-Stokes then Burnett and super-Burnett equations. Navier-Stokes is correct for weak shocks, weak boundary layers and long time asymptotics, but the Burnett equations have spurious high order dispersive effects. In this paper a modified expansion is developed, which combines the best features of the two expansions. It results in nonlinear and linearized Navier-Stokes equations only and is valid in the above-mentioned regimes.

Original languageEnglish (US)
Pages (from-to)701-725
Number of pages25
JournalTransport Theory and Statistical Physics
Issue number4-6
StatePublished - Jun 1 1987


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation
  • Physics and Astronomy(all)
  • Applied Mathematics

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