The fluid dynamic limit of the nonlinear boltzmann equation

Russel Caflisch

Research output: Contribution to journalArticle

Abstract

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
Volume33
Issue number5
DOIs
StatePublished - 1980

Fingerprint

Boltzmann equation
Fluid Dynamics
Fluid dynamics
Boltzmann Equation
Shock
Nonlinear Equations
Compressible Flow
Gas Flow
Error term
Remainder
Ludwig Boltzmann
Euler Equations
Hilbert
Boundary Layer
Euler equations
Iteration
Nonlinear equations
Flow of gases
Boundary layers
Knowledge

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

The fluid dynamic limit of the nonlinear boltzmann equation. / Caflisch, Russel.

In: Communications on Pure and Applied Mathematics, Vol. 33, No. 5, 1980, p. 651-666.

Research output: Contribution to journalArticle

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