Book Review
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MathSciNet review:
3362822
Full text of review:
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Book Information:
Authors:
Isabelle Gallagher,
Laure Saint-Raymond and
Benjamin Texier
Title:
From Newton to Boltzmann: hard spheres and short-range potentials
Additional book information:
Z\"{u}rich Lectures in Advanced Mathematics,
European Mathematical Society,
Z\"{u}rich,
2013,
xii+137 pp.,
ISBN 978-3-03719-129-3
G. Basile, A. Nota, F. Pezzotti and M. Pulvirenti, Derivation of the Fick’s law for the Lorentz model in a low density regime, to appear in Comm. Math. Phys.
T. Bodineau, I. Gallagher and L. Saint-Raymond The Brownian motion as the limit of a deterministic system of hard spheres. arXiv:1305.3397.
N. N. Bogolyubov. “Problems of dynamical theory in statistical physics”, in Studies in Statistical Mechanics (J. de Boer and G. E. Uhlenbeck, Eds.), Interscience, New York, 1962.
Carlo Cercignani, On the Boltzmann equation for rigid spheres, Transport Theory Statist. Phys. 2 (1972), no. 3, 211–225. MR 449375, DOI 10.1080/00411457208232538
I. Gallagher, L. Saint-Raymond and B. Texier, Erratum to Chapter 5 of “From Newton to Boltzmann: hard spheres and short-range potentials”, Zürich Adv. Lect. in Math. Ser., European Mathematical Society (EMS), Zürich, 2014.
Harold Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math. 2 (1949), 331–407. MR 33674, DOI 10.1002/cpa.3160020403
Harold Grad, Principles of the kinetic theory of gases, Handbuch der Physik, Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958. Herausgegeben von S. Flügge. MR 0135535
Francis Gordon King, BBGKY HIERARCHY FOR POSITIVE POTENTIALS, ProQuest LLC, Ann Arbor, MI, 1975. Thesis (Ph.D.)–University of California, Berkeley. MR 2625983
Oscar E. Lanford III, Time evolution of large classical systems, Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974) Lecture Notes in Phys., Vol. 38, Springer, Berlin, 1975, pp. 1–111. MR 0479206
M. Pulvirenti, C. Saffirio, and S. Simonella, On the validity of the Boltzmann equation for short range potentials, Rev. Math. Phys. 26 (2014), no. 2, 1450001, 64. MR 3190204, DOI 10.1142/S0129055X14500019
M. Pulvirenti and S. Simonella, The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error. arXiv:1405.4676.
Sergio Simonella, Evolution of correlation functions in the hard sphere dynamics, J. Stat. Phys. 155 (2014), no. 6, 1191–1221. MR 3207735, DOI 10.1007/s10955-013-0905-7
H. Spohn, Large scale dynamics of interacting particles, Texts and Monographs in Physics, Springer-Verlag, Heidelberg, 1991.
References
- G. Basile, A. Nota, F. Pezzotti and M. Pulvirenti, Derivation of the Fick’s law for the Lorentz model in a low density regime, to appear in Comm. Math. Phys.
- T. Bodineau, I. Gallagher and L. Saint-Raymond The Brownian motion as the limit of a deterministic system of hard spheres. arXiv:1305.3397.
- N. N. Bogolyubov. “Problems of dynamical theory in statistical physics”, in Studies in Statistical Mechanics (J. de Boer and G. E. Uhlenbeck, Eds.), Interscience, New York, 1962.
- Carlo Cercignani, On the Boltzmann equation for rigid spheres, Transport Theory Statist. Phys. 2 (1972), no. 3, 211–225. MR 0449375 (56 \#7679)
- I. Gallagher, L. Saint-Raymond and B. Texier, Erratum to Chapter 5 of “From Newton to Boltzmann: hard spheres and short-range potentials”, Zürich Adv. Lect. in Math. Ser., European Mathematical Society (EMS), Zürich, 2014.
- Harold Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math. 2 (1949), 331–407. MR 0033674 (11,473a)
- Harold Grad, Principles of the kinetic theory of gases, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1958, pp. 205–294. MR 0135535 (24 \#B1583)
- Francis Gordon King, BBGKY hierarchy for positive potentials, ProQuest LLC, Ann Arbor, MI, 1975. Thesis (Ph.D.), University of California, Berkeley. MR 2625983
- Oscar E. Lanford III, Time evolution of large classical systems, Dynamical systems, theory and applications (Rencontres, Battelle Res. Inst., Seattle, Wash., 1974) Springer, Berlin, 1975, pp. 1–111. Lecture Notes in Phys., Vol. 38. MR 0479206 (57 \#18653)
- M. Pulvirenti, C. Saffirio, and S. Simonella, On the validity of the Boltzmann equation for short range potentials, Rev. Math. Phys. 26 (2014), no. 2, 1450001, 64. MR 3190204, DOI 10.1142/S0129055X14500019
- M. Pulvirenti and S. Simonella, The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error. arXiv:1405.4676.
- Sergio Simonella, Evolution of correlation functions in the hard sphere dynamics, J. Stat. Phys. 155 (2014), no. 6, 1191–1221. MR 3207735, DOI 10.1007/s10955-013-0905-7
- H. Spohn, Large scale dynamics of interacting particles, Texts and Monographs in Physics, Springer-Verlag, Heidelberg, 1991.
Review Information:
Reviewer:
Sergio Simonella
Affiliation:
WIAS Berlin
Email:
simonell@wias-berlin.de
Reviewer:
Herbert Spohn
Affiliation:
TU München
Email:
spohn@ma.tum.de
Journal:
Bull. Amer. Math. Soc.
52 (2015), 533-538
DOI:
https://doi.org/10.1090/S0273-0979-2015-01488-6
Published electronically:
February 19, 2015
Review copyright:
© Copyright 2015
American Mathematical Society
