Abstract
An example is given of a model dynamics for which the Broadwell model of the Boltzmann equation seems to appear in the formal stage of the Boltzmann-Grad limit, but actually does not.
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References
K. Alexander, Ph.D. dissertation, Department of Mathematics, University of California at Berkeley (1975).
J. E. Broadwell,J. Fluid. Mech. 19:401 (1964).
C. Cercignani,Theory and Application of the Boltzmann Equation (Scottish Academic Press, Edinburgh, 1975).
H. Grad, Principles of the kinetic theory of gases, inHandbuch der Physik, Vol. 12, F. Flügge, ed. (Springer, Berlin, 1958).
R. Illner and M. Pulvirenti,Commun. Math. Phys. 105:189 (1986).
S. Kawashima,Proc. Japan Acad. 57:19 (1981).
O. E. Lanford, inDynamical Systems and Applications, J. Moser, ed. (Springer, Berlin, 1975).
T. Nishida and M. Mimura,Proc. Japan Acad. 50:812 (1974).
H. Spohn, On the integrated form of the BBGKY hierarchy for hard spheres, preprint.
K. Uchiyama, inProbabilistic Methods in Mathematical Physics, K. Ito and N. Ikeda, eds. (Kinokuniya, Tokyo, 1987).
K. Uchiyama, Derivation of the Boltzmann equation from particle dynamics,Hiroshima Math. J. 18:245–297 (1988).
K. Uchiyama, A tagged particle process in the Boltzmann-Grad limit for the Broadwell model, preprint.
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Uchiyama, K. On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation. J Stat Phys 52, 331–355 (1988). https://doi.org/10.1007/BF01016418
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DOI: https://doi.org/10.1007/BF01016418