Journal of Statistical Physics

, Volume 3, Issue 1, pp 47–68 | Cite as

Existence theory of the linear equations appearing in the Chapman-Enskog solutions to two kinetic equations for liquids

  • H. Ted Davis
  • Marc O. Baleiko
Articles

Abstract

The linear operators appearing in the Chapman-Enskog solutions to Kirkwood's Fokker-Planck kinetic equation and to Rice and Allnatt's kinetic equation are studied in this article. Existence proofs are given for the linearized Chapman-Enskog equations involving either the Fokker-Planck or the Rice-Allnatt operators. It is shown that the Fokker-Planck and Rice-Allnatt operators, defined in the domain appropriate to kinetic theory, are essentially self-adjoint. It is also shown that the spectrum of either of these operators coincides with the spectrum of the self-adjoint extension of the corresponding operator.

Key words

Kinetic theory nonequilibrium statistical mechanics Fokker-Planck and Rice-Allnatt equations existence theory for Chapman-Enskog solutions to kinetic equations 

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Copyright information

© Plenum Publishing Corporation 1971

Authors and Affiliations

  • H. Ted Davis
    • 1
  • Marc O. Baleiko
    • 2
  1. 1.Departments of Chemical Engineering and ChemistryUniversity of MinnesotaMinneapolis
  2. 2.Department of Chemical EngineeringUniversity of MinnesotaMinneapolis

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