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Nonequilibrium phenomena I: The Boltzmann equation. (English) Zbl 0583.76004
Studies in Statistical Mechanics, Vol. X. Amsterdam-New York-Oxford: North-Holland Publishing Company. VII, 254 p. S 40.00; Dfl. 120.00 (1983).
This volume comprises a series of 6 review articles devoted to various aspects of the foundations and the mathematics underlying applications of the Boltzmann equation (BE). O. E. Lanford III discusses theorems concerned with the derivation of the BE. Global existence proofs of the BE are presented by W. Greenberg, J. Polewczak and P. F. Zweifel. A review on exact solutions of the nonlinear BE is given by M. H. Ernst; nonconventional applications to chemical kinetics and polymerisation dynamics are discussed. Under the heading ”Solution of the BE”, C. Cercignani presents methods for the treatment of initial and boundary value problems, of special interest is the transition from the hydrodynamic to the Knudsen regime. The article by R. E. Caflisch is devoted to fluid dynamics as studied via the Boltzmann equation. H. Spohn is concerned with extensions of the BE needed to treat fluctuation phenomena. The book is considered quite useful for experts in the field; newcomers are advised also to consult the classic articles by H. Grad [in: S. Flügge (ed.), Encyclopedia of Physics, Springer, Berlin-Göttingen-Heidelberg (1958) on pp. 205-294] and by L. Waldmann [in: ibid. on pp 295-514] in the Handbuch der Physik, vol. 12.
Reviewer: S.Hess

76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35Q99 Partial differential equations of mathematical physics and other areas of application
82B40 Kinetic theory of gases in equilibrium statistical mechanics