The Linearized Collision Operator

  • Carlo Cercignani


In Chapter II we found a solution of the Boltzmann equation, i.e., the Maxwellian. It is an exact solution of the Boltzmann equation and the most significant and widely used solution [other interesting solutions have been found but there is not sufficient space to discuss them here; some of them are discussed in detail in a book by Truesdell and Muncaster (ref. 1); see also Chapter VII, Section 14]. The meaning of the Maxwellian distribution is clear: it describes equilibrium states (or slight generalizations of them), characterized by the fact that neither heat flow nor stresses other than isotropic pressure are present. If we want to describe more realistic non-equilibrium situations, when oblique stresses are present and heat transfers take place, we have to rely upon approximation methods.


Boltzmann Equation Collision Operator Rigid Sphere Complete Continuity Collision Invariant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s Kinetic Theory of a Simple Monatomic Gas, Academic Press, New York (1980).Google Scholar
  2. 2.
    H. Grad, in: Rarefied Gas Dynamics (J. A. Laurmann, ed.), Vol. I, p. 100, Academic Press, New York (1963);Google Scholar
  3. 3.
    D. Hilbert, Math. Ann. 72, 562 (1912).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    F. Riesz and B. Sz-Nagy, Functional Analysis (translated by L. Boron), Frederick Ungar, New York (1955).Google Scholar
  5. 5.
    I. Kuščcer and M. M. R. Williams, Phys. Fluids 10, 1922 (1967);CrossRefGoogle Scholar
  6. 6.
    O. O. Jenssen, Phys. Norvegica 6, 179 (1972);MathSciNetGoogle Scholar
  7. 7.
    Y. P. Pao, in Rarefied Gas Dynamics (M. Becker and M. Fiebig, eds.), Vol. I, p. A.6-1, DFVLR Press, Porz-Wahn (1974);Google Scholar
  8. 8.
    Y. P. Pao, Commun. Pure Appl. Math. 27, 407 (1974);MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Y. P. Pao, Commun. Pure Appl. Math. 27, 559 (1974);MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Klaus, Helv. Phys. Acta 50, 893 (1977).MathSciNetGoogle Scholar
  11. 11.
    C. Cercignani, Phys. Fluids 10, 2097 (1967)CrossRefGoogle Scholar
  12. 12.
    H. Drange, SIAM J. Appl. Math. 29, 4 (1975).MathSciNetCrossRefGoogle Scholar
  13. 13.
    C. S. Wang Chang and G. E. Uhlenbeck, ‘On the Propagation of Sound in Monatomic Gases, University of Michigan Press, Project M999, Ann Arbor, Michigan (1952).Google Scholar
  14. 14.
    Bateman Manuscript Project, Higher Transcendental Functions, Vol. II, McGraw-Hill, New York (1953), pp. 64 and 188.Google Scholar
  15. 15.
    H. M. Mott-Smith, “A New Approach in the Kinetic Theory of Gases,” MIT Lincoln Laboratory Group Report V-2 (1954).Google Scholar

Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Carlo Cercignani
    • 1
  1. 1.Politecnico di MilanoMilanItaly

Personalised recommendations