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Microscopic Derivation of the Boltzmann Equation

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Book cover Kinetic Theory and Gas Dynamics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 293))

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Abstract

Up to date (1987), I list references on the rigorous microscopic derivation of the Boltzmann equation from the mechanical model of hard sferes with elastic collisions, resp. of classical particles interacting through a smooth pair potential.

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References

  1. O.E. Lanford, Time evolution of large classical systems, In: Dynamical Systems and Applications, ed. J. Moser, Lecture Notes in Physics Vol. 38, 1–111. Springer, Berlin, 1975.

    Google Scholar 

  2. O.E. Lanford, On a derivation of the Boltzmann equation, Astérisque, 40, 117–137 (1976)

    MathSciNet  Google Scholar 

  3. Nonequilibrium Phenomena I, The Boltzmann Equation, eds. J.L. Lebowitz and E.W. Montroll, Studies in Statistical Mechanics X, North-Holland, Amsterdam, 1983.

    Google Scholar 

  4. O.E. Lanford, Notes of the lectures at the troisième cycle at Lausanne, 1978, unpublished.

    Google Scholar 

  5. O.E. Lanford, Hard-sphere gas in the Boltzmann-Grad limit, Physica 106A, 70–76 (1981).

    Article  Google Scholar 

  6. F. King, BBGKY hierarchy for positive potentials, PH. D. thesis, Dept. of Mathematics, Univ. of California at Berkeley, 1975.

    Google Scholar 

  7. R. Illner and M. Pulvirenti, A derivation of the BBGKY-hierarchy for hard sphere particle systems, preprint Univ. of Victoria, 1985, to appear in Transport Theory and Statistical Physics:

    Google Scholar 

  8. H.Spohn, On the integrated form of the BBGKY hierarchy for hard spheres, preprint.

    Google Scholar 

  9. K. Uchiyama, On the derivation of the Boltzmann equation from a deterministic motion of many particles, Taniguchi Symp. PMMP Katata 1985, p. 421–441.

    Google Scholar 

  10. K. Uchiyama, Derivation of the Boltzmann equation from particle dynamics, preprint, 1987. The technical machinery developed in [1] and [6] has been used to tackle related problems. (i) fluctuation theory for the Boltzmann equation.

    Google Scholar 

  11. H. van Beijeren, O.E. Lanford, J.L. Lebowitz, H. Spohn, Equilibrium time correlation functions in the low density limit, J. Stat. Phys. 22, 237–257 (1980).

    Article  MATH  Google Scholar 

  12. H. Spohn, Fluctuations around the Boltzmann equation, J. Stat. Phys. 26, 285–305 (1981).

    Article  MathSciNet  Google Scholar 

  13. H. Spohn, Fluctuation theory for the Boltzmann equation, in [3].

    Google Scholar 

  14. H. Spohn, Boltzmann equation and Boltzmann hierarchy. In “Kinetic Theories and the Boltzmann Equation”, eds. C. Cercignani, Lecture Notes in Math. 1048, p. 207–220, Springer, Berlin, 1984.

    Chapter  Google Scholar 

  15. G. Gallavotti, Rigorous theory of the Boltzmann equation in the Lorentz gas, Nota interna n. 358, Univ. di Roma and Phys. Rev. 185, 308 (1969).

    Google Scholar 

  16. H. Spohn, The Lorentz process converges to a random flight process, Comm. Math. Phys. 60, 277–290 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  17. H. Babovsky, Diplomarbeit, Univ. Kaiserslautern, 1980.

    Google Scholar 

  18. J.L. Lebowitz and H. Spohn, Steady state self-diffusion at low density, J. Stat. Phys. 29, 39–55, (1982).

    Article  MATH  MathSciNet  Google Scholar 

  19. C. Boldrighini, L.A. Bunimovich, Y.G. Sinai, On the Boltzmann equation for the Lorentz gas, J. Stat. Phys. 32, 477 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  20. R. Illner and M. Pulvirenti, Global validity of the Boltzmann equation for a two-dimensional rare gas in vacuum, Comm. Math. Phys. 105, 189–203 (1986).

    Article  MATH  MathSciNet  Google Scholar 

  21. M. Pulvirenti, Global validity of the Boltzmann equation for a three-dimensional rare gas in vacuum, Comm. Math. Phys. 113, 79–85 (1987).

    Article  MATH  MathSciNet  Google Scholar 

  22. J.L. Lebowitz and H. Spohn, On the time evolution of macroscopic systems, Comm. Pure Appl. Math. 36, 593–613 (1983).

    MathSciNet  Google Scholar 

  23. C. Cercignani, The Grad limit for a system of soft spheres, Comm. Pure Appl. Math. 36, 479–494 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  24. K. Uchiyama, On the Boltzmann-Grad limit for the Broadwell of the Boltzmann equation, preprint, 1987.

    Google Scholar 

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© 1988 Springer-Verlag Wien

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Spohn, H. (1988). Microscopic Derivation of the Boltzmann Equation. In: Cercignani, C. (eds) Kinetic Theory and Gas Dynamics. International Centre for Mechanical Sciences, vol 293. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2762-9_7

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  • DOI: https://doi.org/10.1007/978-3-7091-2762-9_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82090-2

  • Online ISBN: 978-3-7091-2762-9

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