Il sesto problema di Hilbert e le moderne teorie cinetiche.

Mario Pulvirenti

Bollettino dell'Unione Matematica Italiana (2004)

  • Volume: 7-B, Issue: 3, page 545-562
  • ISSN: 0392-4041

Abstract

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We discuss some problems arising in the attempts of deriving kinetic equations from the mechanics of particle systems.

How to cite

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Pulvirenti, Mario. "Il sesto problema di Hilbert e le moderne teorie cinetiche.." Bollettino dell'Unione Matematica Italiana 7-B.3 (2004): 545-562. <http://eudml.org/doc/194915>.

@article{Pulvirenti2004,
abstract = {In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.},
author = {Pulvirenti, Mario},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {ita},
month = {10},
number = {3},
pages = {545-562},
publisher = {Unione Matematica Italiana},
title = {Il sesto problema di Hilbert e le moderne teorie cinetiche.},
url = {http://eudml.org/doc/194915},
volume = {7-B},
year = {2004},
}

TY - JOUR
AU - Pulvirenti, Mario
TI - Il sesto problema di Hilbert e le moderne teorie cinetiche.
JO - Bollettino dell'Unione Matematica Italiana
DA - 2004/10//
PB - Unione Matematica Italiana
VL - 7-B
IS - 3
SP - 545
EP - 562
AB - In questo contributo si discute qualche problema connesso alla derivazione delle equazioni cinetiche a partire dalla meccanica dei sistemi di particelle.
LA - ita
UR - http://eudml.org/doc/194915
ER -

References

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  1. BOLDRIGHINI, C.- BUNIMOVICH, C.- SINAI, YA., On the Boltzmann equation for the Lorentz gas, J. Stat. Phys., 32 (1983), 477-501. Zbl0583.76092MR725107
  2. BUNIMOVICH, L. A.- SINAI, YA. G., Statistical properties of the Lorentz gas with periodic configuration of scatterers, Comm. Math. Phys., 78 (1981), 478-497. Zbl0459.60099MR606459
  3. BURGAIN, J.- GOLSE, F.- WENNBERG, B., On the distribution of free path lenght for the periodic Lorentz gas, Comm. Math. Phys., 190 (1998), 491-508. Zbl0910.60082MR1600299
  4. CAGLIOTI, E.- PULVIRENTI, M.- RICCI, V., Derivation of a linear Boltzmann equation for a periodic Lorentz gas, Markov Proc. Rel. Fields, 3 (2000), 265-285. Zbl1013.82012MR1784071
  5. CERCIGNANI, C., Ludwig Boltzmann e la Meccanica Statistica, La Goliardica (Pavia), 1998. Zbl1049.82500MR1719677
  6. CERCIGNANI, C., On the Boltzmann equation for rigid spheres, Transp. Theor. Stat. Phys., (1972), 211-225. Zbl0295.76048MR449375
  7. CERCIGNANI, C.- ILLNER, R.- PULVIRENTI, M., The mathematical theory of dilute gases, Springerseries in Appl. Math., vol. 106, 1994. Zbl0813.76001MR1307620
  8. DESVILLETTES, L.- PULVIRENTI, M., The linear Boltzmann equation for longrange forces: a derivation from particle systems, Models Methods Appl. Sci., 9 (1999), 1123-1145. Zbl1010.82019MR1722064
  9. DESVILLETTES, L.- RICCI, V., Rigorous derivation of a linear kinetic equation of Fokker-Plank type in the limit of grazing collisions, Jour. Stat. Phys., 104 (2001), 1173-1189. Zbl1051.82022MR1859001
  10. DI PERNA, R. J.- LIONS, P. L., On the Cauchy problem for the Boltzmann equations: Global existence and weak stability, Annals of Mathematics, 130 (1989), 321-366. Zbl0698.45010MR1014927
  11. ESPOSITO, R.- PULVIRENTI, M., From Particles to Fluids, Handbook of Mathematical Fluid Dynamics, North-Holland, vol. 3, S. Frielander and D. Serre editors, 2004. Zblpre05177019MR2099033
  12. GALLAVOTTI, G., Divergences and approach to equilibrium in the Lorentz and the Wind-tree models, Physical Review, 185 (1969), 308-322. 
  13. GALLAVOTTI, G., Rigorous theory of the Boltzmann equation in the Lorentz gas, reprinted in G. Gallavotti Meccanica Statistica, Quaderni del CNR n. 50, Nota interna n. 358 Istituto di Fisica Università di Roma, 1972 (1995), 191-204. 
  14. GRAD, H., On the kinetic theory of rarified gases, Comm. Pure Appl. Math., 2 (1949), 331-407. Zbl0037.13104MR33674
  15. ILLNER, R.- PULVIRENTI, M., Global validity of the Boltzmann equation for two and three-dimensional rare gas in vacuum: erratum and improved result, Comm. Math. Phys., 121 (1989), 143-146. Zbl0850.76600MR985619
  16. KAC, M., Probability and related topics, Interscience; New York, 1959. 
  17. LANFORD III, O., The evolution of large classical system, Lect. Notes in Physics. Springer, (J. Moser ed.), 35 (1975), 1-111. Zbl0329.70011MR479206
  18. MORREY, C. B., On the derivation of the equations of hydrodynamics from statistical mechanics, Comm. Pure Appl. Math., 8 (1955), 279-326. Zbl0065.19406MR70527
  19. SPOHN, H., The Lorentz flight process converges to a random flight process, Comm. Math. Phys., 60 (1978), 277-290. Zbl0381.60099MR496299
  20. UCHIYAMA, K., On the Boltzmann-Grad limit for the Broadwell model of the Boltzmann equation, J. Statist. Phys., 52 (1988), 331-355. Zbl1083.82532MR968589

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