Shock profile solutions of the Boltzmann equation

Russel 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 1982

Fingerprint

Boltzmann Equation
Shock
shock
profiles
Schmidt method
Bifurcation
Lyapunov-Schmidt Method
gas dynamics
Gas Dynamics
Projection Method
Navier-Stokes
Shock Waves
Euler
shock waves
Navier-Stokes Equations
projection
Profile
expansion
acoustics
Term

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Shock profile solutions of the Boltzmann equation. / Caflisch, Russel; Nicolaenko, Basil.

In: Communications in Mathematical Physics, Vol. 86, No. 2, 06.1982, p. 161-194.

Research output: Contribution to journalArticle

Caflisch, Russel ; Nicolaenko, Basil. / Shock profile solutions of the Boltzmann equation. In: Communications in Mathematical Physics. 1982 ; Vol. 86, No. 2. pp. 161-194.
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