Relativistic gas: Moment equations and maximum wave velocity

Journal of Mathematical Physics

Volumn 40, Issue 12, 1999, Pages 6399-6406

  Boillat, Guy ^a   Ruggeri, Tommaso ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033249098     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533099     Document Type: Article

References (31)

1. C. Eckart, "The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid," Phys. Rev. 58, 919 (1940).
2. I. Müller and T. Ruggeri, Rational Extended Thermodynamics, Springer Tracts in Natural Philosophy, Vol. 37, 2nd ed. (Springer, New York, 1998).
3. C. Cattaneo, "Sulla conduzione del calore," Atti Sem. Mat. Fis, Univ. Modena 3, 83 (1948-1949).
4. I. Müller, "Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien," dissertation Aachen, 1966.
5. W. Israel, "Nonstationary irreversible thermodynamics: A causal relativistic theory," Ann Phys. (N.Y.) 100, 341 (1976).
6. I-Shih Lin, I. Müller, and T. Ruggeri, "Relativistic thermodynamics of gases," Ann. Phys. (N.Y.) 169, 191 (1986).
7. C. Marie, "Sur l'établissement des équations de l'hydrodynamique des fluides relativistes dissipatives," Ann. Inst. Henri Poincare 10, 67 (1969).
8. N. A. Chernikov, "The relativistic gas in the gravitational field," Acta Phys. Pol. 23, 629 (1963); "Equilibrium distribution of the relativistic gas," 26, 379 (1964); "Microscopic foundation of relativistic hydrodynamics," 27, 465 (1965).
9. N. A. Chernikov, "The relativistic gas in the gravitational field," Acta Phys. Pol. 23, 629 (1963); "Equilibrium distribution of the relativistic gas," 26, 379 (1964); "Microscopic foundation of relativistic hydrodynamics," 27, 465 (1965).
10. N. A. Chernikov, "The relativistic gas in the gravitational field," Acta Phys. Pol. 23, 629 (1963); "Equilibrium distribution of the relativistic gas," 26, 379 (1964); "Microscopic foundation of relativistic hydrodynamics," 27, 465 (1965).
11. G. Boillat and T. Ruggeri, "Moment equations in the kinetic theory of gases and wave velocities," Continuum Mech. Thermodyn. 9, 205 (1997).
12. G. Boillat and T. Ruggeri, "Maximum wave velocity in the moment system of a relativistic gas," Continuum Mech. Thermodyn. 11, 107 (1999).
13. I. Müller, Speeds of Propagation in Classical and Relativistic Extended Thermodynamics, Living Reviews in Relativity (Max-Planck-Institute for Gravitational Physics, Albert Einstein Institute, Potsdam, 1999), http://www.livingreviews.org/ Articles/Volume2/1999-1mueller/
14. A. Lichnerowicz and R. Manot, "Propriétés statistiques des ensembles de particules en relativité restreinte," C. R. Acad. Sci. 210, 759 (1940); "Sur l'équation intégrodifférentielle de Boltzmann," 211, 531 (1940); "Le H-théorême et la notion de système isolé," 212, 1074 (1941).
15. A. Lichnerowicz and R. Manot, "Propriétés statistiques des ensembles de particules en relativité restreinte," C. R. Acad. Sci. 210, 759 (1940); "Sur l'équation intégrodifférentielle de Boltzmann," 211, 531 (1940); "Le H-théorême et la notion de système isolé," 212, 1074 (1941).
16. A. Lichnerowicz and R. Manot, "Propriétés statistiques des ensembles de particules en relativité restreinte," C. R. Acad. Sci. 210, 759 (1940); "Sur l'équation intégrodifférentielle de Boltzmann," 211, 531 (1940); "Le H-théorême et la notion de système isolé," 212, 1074 (1941).
17. G. Boillat, "Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systèmes hyperboliques," C. R. Acad. Sci. Paris 278A, 909 (1974); Nonlinear Fields and Waves in CIME Course Recent Mathematical Methods in Nonlinear Wave Propagation, edited by T. Ruggeri, Lecture Notes in Mathematics Vol. 1640 (Springer, Berlin, 1996).
18. G. Boillat, "Sur l'existence et la recherche d'équations de conservation supplémentaires pour les systèmes hyperboliques," C. R. Acad. Sci. Paris 278A, 909 (1974); Nonlinear Fields and Waves in CIME Course Recent Mathematical Methods in Nonlinear Wave Propagation, edited by T. Ruggeri, Lecture Notes in Mathematics Vol. 1640 (Springer, Berlin, 1996).
19. T. Ruggeri and A. Strumia, "Main field and convex covariant density for quasi-linear hyperbolic systems. Relativistic fluid dynamics," Ann. Inst. Henri Poincare, Sect. A 34, 65 (1981).
20. W. Dreyer, "Maximisation of the Entropy in Non-Equilibrium," J. Phys. A 20, 6505 (1987).
21. M. N. Kogan, Proceedings of the Fifth Symposium on Rarefied Gas Dynamics (Academic, New York, 1967), Vol. 1, suppl. 4, pp. 359-368.
22. E. T. Jaynes, "Information theory and statistical mechanics I, II," Phys. Rev. 106, 620 (1957); 108, 171 (1957).
23. E. T. Jaynes, "Information theory and statistical mechanics I, II," Phys. Rev. 106, 620 (1957); 108, 171 (1957).
24. J. N. Kapur, Maximum-Entropy Models in Science and Engineering (Wiley, New York, 1989); H. Gzyl, The Method of Maximum Entropy (World Scientific, Singapore, 1995).
25. J. N. Kapur, Maximum-Entropy Models in Science and Engineering (Wiley, New York, 1989); H. Gzyl, The Method of Maximum Entropy (World Scientific, Singapore, 1995).
26. A. E. Fisher and J. E. Marsden, "The Einstein evolution equations as a first order quasilinear symmetric hyperbolic system," Commun. Math. Phys. 28, 1 (1972).
27. G. Boillat and T. Ruggeri, "Hyperbolic principal subsystems: entropy convexity and subcharacteristic conditions," Arch. Ration. Mech. Anal. 137, 305 (1997).
28. G. Boillat and T. Ruggeri, "On the shock structure problem for hyperbolic system of balance laws and convex entropy," Continuum Mech. Thermodyn. 10, 285 (1998).
29. F. Jüttner, "Das Maxwell'sche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie," Ann. Phys. (Leipzig) 34, 856 (1911); "Die relativistische Quantentheorie des idealen Gases," Z. Phys. 47, 542 (1928).
30. F. Jüttner, "Das Maxwell'sche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie," Ann. Phys. (Leipzig) 34, 856 (1911); "Die relativistische Quantentheorie des idealen Gases," Z. Phys. 47, 542 (1928).
31. F. Brini and T. Ruggeri, "Maximum velocity for wave propagation in a relativistic gas," Continuum Mech. Thermodyn. 11, 331 (1999).