Skip to main content
Log in

On the normal solutions of the Boltzmann equation with small Knudsen number

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

A singular perturbation method is used to find the normal solutions of the Boltzmann equation with small Knudsen number. It is proved that the secular terms may be removed by improving the Hilbert expansion and the Enskog expansion.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. C. Cercignani,Theory and Application of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975).

    Google Scholar 

  2. A. V. Bobylev,Sov. Phys. Dokl. 20:822 (1975).

    Google Scholar 

  3. M. Krook and T. T. Wu,Phys. Rev. Lett. 36:1107 (1976).

    Google Scholar 

  4. E. H. Hauge and E. Praestagaard,J. Stat. Phys. 24:21 (1981).

    Google Scholar 

  5. H. Grad,Commun. Pure Appl. Math. 2:33 (1949).

    Google Scholar 

  6. P. L. Bhatnagar, E. P. Gross, and M. Krook,Phys. Rev. 94:511 (1954).

    Google Scholar 

  7. G. A. Bird,Molecular Gas Dynamics (Clarenden Press, Oxford, 1976).

    Google Scholar 

  8. D. Hilbert,Math. Ann. 72:562 (1912).

    Google Scholar 

  9. S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, 1970).

    Google Scholar 

  10. A. V. Bobylev,Sov. Phys. Dokl. 20:820 (1975).

    Google Scholar 

  11. C. S. Wang Chang and G. E. Uhlenbeck, The kinetic theory of gases, inStudies in Statistical Mechanics, Vol. V, J. de Boer and G. E. Uhlenbeck, eds. (North-Holland, Amsterdam, 1970).

    Google Scholar 

  12. A. V. Bobylev,Sov. Phys. Dokl. 27:29 (1982).

    Google Scholar 

  13. T. F. Morse,Phys. Fluids 7:1691 (1964).

    Google Scholar 

  14. L. Trilling,Phys. Fluids 7:1681 (1964).

    Google Scholar 

  15. E. J. Ding and Z. Q. Huang,J. Stat. Phys., this issue, following paper.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, E.J., Huang, Z.Q. On the normal solutions of the Boltzmann equation with small Knudsen number. J Stat Phys 45, 561–588 (1986). https://doi.org/10.1007/BF01021086

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01021086

Key words

Navigation