Trend to equilibrium of a degenerate relativistic gas

Journal of Statistical Physics

Volumn 98, Issue 1-2, 2000, Pages 441-456

  Cercignani, C ^a   Kremer, G M ^b  

^a POLITECNICO DI MILANO   (Italy)

^b FEDERAL UNIVERSITY OF PARANÁ   (Brazil)

Author keywords

Kinetic theory; Relativity; Trend to equilibrium

Indexed keywords

EID: 0034341503     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018695426728     Document Type: Article

References (26)

1. C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas (Academic Press, New York, 1980).
2. T. Carleman, Sur la théorie de l'équation intégro-differentielle de Boltzmann, Acta Mathematica 60:91-146 (1933).
3. T. Carleman, Problèmes mathématiques dans la théorie cinétique des gaz (Almqvist & Wiksells, Uppsala, 1957).
4. D. Morgenstern, General existence and uniqueness proof for spatially homogeneous solutions of the Maxwell-Boltzmann equation in the case of Maxwellian molecules, Proceedings of the National Academy of Sciences (U.S.A.) 40:719-721 (1954).
5. L. Arkeryd, On the Boltzmann equation. Part I: Existence, Arch. Rat. Mech. Anal. 45:1-16 (1972).
6. L. Arkeryd, On the Boltzmann equation. Part II: The full initial value problem, Arch. Rat. Mech. Anal. 45:17-34 (1972).
7. ∞ estimates for the space-homogeneous Boltzmann equation, J. Stat. Phys. 31:347-361 (1983).
8. C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases (Springer, New York, 1994).
9. E. A. Uehling, and G. E. Uhlenbeck, Transport phenomena in Einstein Bose and Fermi Dirac gases. I, Phys. Rev. 43:552-561 (1933).
10. S. Chapman, and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, London, 1940).
11. J. Dolbeault, Kinetic models and quantum effects: A modified Boltzmann equation for Fermi Dirac particles, Arch. Ration. Mech. Anal. 127:101-131 (1994).
12. P. L. Lions, Compactness in Boltzmann's equation via Fourier integral operator and applications III, J. Math. Kyoto Univ. 34:539-584 (1994).
13. X. Lu, Global Isotropic Solutions of a Modified Boltzmann Equation or Bose Einstein Particles, Presented at the XVI International Conference on Transport Theory (Atlanta. May 10 15, 1999).
14. 1 convergence to equilibrium for the relativistic Boltzmann equation. SIAM Math. Anal. 27:1387-1405 (1996).
15. R. Glassey and W. Strauss, Asymptotic stability of the relativistic equilibrium, Publ. Res. Inst. Math. Sci. 29:301-347 (1992).
16. C. Cercignani and G. M. Kremer, On relativistic collisional invariants, J. Stat. Phys. (to appear, 1999).
17. F. Jüttner, Das Maxwellsche gesetz der geschwindigkeitsverteilung in der relativtheorie, Ann. Physik Chemie 34:856-882 (1911).
18. F. Jüttner, Die relativistische quantentheorie des idealen gases, Zeitschr. Physik 47:542-566 (1928).
19. C. Cercignani, Ludwig Boltzmann. The Man Who Trusted Atoms (Oxford University Press, Oxford, 1998).
20. C. Cercignani, H-theorem and trend to equilibrium in the kinetic theory of gases, Arch. Mech. 34:231-241 (1982).
21. A. V. Bobylev, Exact solutions of the Boltzmann equation and the theory of relaxation of Maxwell gas, USSR Theor. Math. Phys. 60:280-310 (1984).
22. E. A. Carlen and M. C. Carvalho, The central limit theorem, entropy production and stability of the rate of convergence for the Boltzmann equation, in Probabilistic Methods in Mathematical Physics, F. Guerra, M. I. Loffredo, and C. Marchioro, eds. (World Scientific, Singapore, 1992), pp. 140-154.
23. E. A. Marten and M. C. Carvalho, Entropy production estimates for Boltzmann equations with physically realistic collision kernels, J. Stat. Phys. 74:743-782 (1994).
24. B. Wennberg, Entropy dissipation and moment production for the Boltzmann equation, J. Stat. Phys. 86:1053-1066 (1997).
25. A. V. Bobylev and C. Cercignani, On the rate of entropy production for the Boltzmann equation, J. Stat. Phys. (to appear, 1999).
26. G. Toscani and C. Villani, Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation, submitted to Comm. Math. Phys. (1998).