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The Boltzmann-Landau transport equation

I. The first-order Chapman-Enskog approximation

Published online by Cambridge University Press:  24 October 2008

Arun K. Mitra
Affiliation:
Department of Mathematics, Texas Technological College, Lubbock, Texas
Sunanda Mitra
Affiliation:
Department of Mathematics, Texas Technological College, Lubbock, Texas

Abstract

The first-order Chapman-Enskog (CE) approximation has been used to linearize the Boltzmann-Landau (BL) equation primarily in the binary collision approximation and a linear integral equation with a non-symmetric kernel is obtained. The solubility conditions are discussed on the basis of conservation theorems. The formal solutions and the transport coefficients have been obtained in a subsequent paper.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Cohen, E. G. D.Fundamental problems in statistical mechanics (North Holland Publishing Co., Amsterdam, 1962).CrossRefGoogle Scholar
Uhlenbeck, G. E. and Ford, G. W.Lectures in statistical mechanics (American Mathematical Society, 1963).Google Scholar
(2)Kawasaki, K. and Oppenheim, I.Phys. Rev. A 136 (1964), 1519; Phys. Rev. A 139 (1964), 649.CrossRefGoogle Scholar
(3)Ernst, M. H., Dorfman, J. R. and Cohen, E. G. D.Physica 31 (1965), 493.CrossRefGoogle Scholar
(4)Ernst, M. H.Physica 32 (1966), 209.Google Scholar
(5)Cohen, E. G. D. and Dorfman, J. R.Phys. Lett. 16 (1965), 124.CrossRefGoogle Scholar
(6)Sengers, L. V.Phys. Rev. Lett. 15 (1965), 515.CrossRefGoogle Scholar
(7)Kawasaki, K. and Oppenheim, I.Phys. Rev. A 139 (1965), 1763.CrossRefGoogle Scholar
(8)Landau, L. D.Soviet Physics, JETP 3 (1957), 920; 5 (1957), 101; 8 (1959), 70.Google Scholar
(9)Grossmann, S. (a) Z. Physik 82 (1964), 24; (b) Nuovo Cimento 37 (1964), 698; (c) Z. Naturforsch. 20a (1965), 861.Google Scholar
(10)Huang, K.Statistical mechanics (John Wiley and Sons, Inc., New York, London, 1963).Google Scholar
(11)Chapman, S. and Cowling, T. G.Mathematical theory of non-uniform gases (Cambridge University Press, 1953).Google Scholar
(12)Lovitt, W. V.Linear integral equations (Dover Publ. Inc., New York, 1950).Google Scholar