The fluid dynamic limit of the nonlinear boltzmann equation

Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review


Solutions of the nonlinear Boltzmann equation are constructed up to the first appearance of shocks in the corresponding fluid dynamics. This construction assumes the knowledge of solutions of the Euler equations for compressible gas flow. The Boltzmann solution is found as a truncated Hilbert expansion with a remainder, and the remainder term solves a weakly nonlinear equation which is solved by iteration. The solutions found have special initial values. They should serve as “outer expansions” to which initial layers, boundary layers and shock layers can be matched.

Original languageEnglish (US)
Pages (from-to)651-666
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - Sep 1980

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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