Shock profile solutions of the Boltzmann equation

Russel E. Caflisch, Basil Nicolaenko

Research output: Contribution to journalArticle

Abstract

Shock waves in gas dynamics can be described by the Euler Navier-Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which are weak. The shock is written as a truncated expansion in powers of the shock strength, the first two terms of which come exactly from the Taylor tanh (x) profile for the Navier-Stokes solution. The full solution is found by a projection method like the Lyapunov-Schmidt method as a bifurcation from the constant state in which the bifurcation parameter is the difference between the speed of sound c0 and the shock speed s.

Original languageEnglish (US)
Pages (from-to)161-194
Number of pages34
JournalCommunications In Mathematical Physics
Volume86
Issue number2
DOIs
StatePublished - Jun 1 1982

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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