Abstract
In the previous chapter we saw that the problem of describing the state of thermal equilibrium of a monatomic perfect gas can be nicely solved; in particular, we found a very simple formula for the one-particle distribution P (1) in the form of a Maxwellian. This result has a large variety of applications in the statistical description of matter in the gaseous state.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. Chapman and T. G. Cowling, “The Mathematical Theory of Nonuniform Gases,” Cambridge University Press, Cambridge (1952).
J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, “Molecular Theory of Gases and Liquids/1 Wiley, New York (1954).
L. Waldmann, in “Handbuch der Physik”, vol. XII, p. 384, Springer Verlag, Berlin (1958).
L. Boltzmann, “Lectures on Gas Theory” (English translation from the German), University of California Press, Berkeley (1964).
T. Carleman, “Problemes Mathematiques dans la Theorie Cinetique des Gas”, Almqvist and Wiksells, Uppsala (1957).
J. Jeans, “Dynamical Theory of Gases,” Dover, New York (1954).
M. N. Kogan, “Rarefied Gas Dynamics,” Plenum Press, New York (1969).
H. Grad, “Comm. Pure Appl. Math.”, 14, 323 (1961).
C. Cercignani, “Transport Theory and Statistical Physics”, 2, 211 (1972).
N. N. Bogoliubov, “Problems of a Dynamical Theory in Statistical Physics,” (English translation from the Russian) in “Studies in Statistical Mechanics”, J. de Boer and G. E. Uhlenbeck, Eds., Vol. I, p. 5, North-Holland Publishing Company, Amsterdam (1962).
M. Born and H. S. Green, “A General Kinetic Theory of Fluids”, Cambridge University Press, Cambridge (1949).
J. G. Kirkwood, “J. Chem. Phys.”, 14,180 (1946).
J. G. Kirkwood, “J. Chem. Phys.”, 15, 72 (1947).
J. Yvon, “La Theorie Statistique des Fluides”, Actualites Scientifiques et Industrielles, no. 203, Hermann, Paris (1935).
H. Grad, in “Handbuch der Physik”, vol. XII, Springer, Berlin (1958).
C. S. Wang Chang, G. E. Uhlenbeck and J. DE Boer, in “Studies in Statistical Mechanics”, J. de Boer and G. E. Uhlenbeck, Eds. vol. II, Part c, North Holland Publishing Company, Amsterdam (1964).
J. C. Maxwell, “Phil. Trans. Roy. Soc.”, 157 (1866); reprinted in: ”The Scientific Papers by J. C. Maxwell”, Dover, New York (1965)
C. Cercignani, “Phys. Fluids”, 10,2097 (1967).
I. Prigogine, “Non-Equilibrium Statistical Mechanics”, Interscience, New York (1962).
R. Balescu, “Statistical Mechanics of Charged Particles”, Interscience, New York (1962).
R, L. Liboff, “Introduction to the Theory of Kinetic Equations”, Wiley, New York (1969).
P. L. Bhatnagar, E. P. Gross and M. Krook, “Phys. Rev.”, 94, 511 (1954).
P. Welander, “Arkiv Fysik”, 7, 507 (1954).
M. Krook, “J. Fluid Mech.”, 6, 523 (1959).
L. H. Holway, JR., Ph.D. Thesis, Harvard (1963).
C. Cercignani and G. Tironi, “in Rarefied Gas Dynamics” (C. L. Brundin, ed.), vol. I, Academic Press, New York (1967), p. 441.
L. Sirovich, “Phys. Fluids”, 5, 908 (1962).
C. Cercignani, “Mathematical Methods in Kinetic Theory”, Plenum Press, New York (1969).
J. L. Lebowitz, H. L. Frisch, and E. Helfand, “Phys. Fluids”, 3, 325 (1960).
T. F. Morse, “Phys. Fluids”, 7, 2012 (1964).
F. B. Hanson and T. F. Morse, “Phys. Fluids”, 10, 345 (1967).
H. Jeffreys, “Asymptotic Approximations”, Oxford University Press, Oxford (1962).
E. Artin, “The Gamma Function”, Holt, Rinehart and Winston, New York (1964).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1988 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cercignani, C. (1988). The Boltzmann Equation. In: The Boltzmann Equation and Its Applications. Applied Mathematical Sciences, vol 67. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1039-9_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1039-9_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6995-3
Online ISBN: 978-1-4612-1039-9
eBook Packages: Springer Book Archive