PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

The relativistic Boltzmann equation - mathematical and physical aspects

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Mathematical structure of the linearized Boltzmann equation is outlined. Physical interpretation of the assumed relativistic cross-sections is discussed.
Rocznik
Strony
39--47
Opis fizyczny
Bibliogr. 35 poz.
Twórcy
  • Modern Technologies and Filtration Ltd., Mokotowska 40/21, 00-543 Warsaw, Poland
Bibliografia
  • 1. L. HSIAO, H.J. Yu, Asymptotic stability of the relativistic Maxwellian, Math. Method Appl. Sci., 29, 1481-1499, 2006.
  • 2. R.T. GLASSEY, Global Solutions to the Cauchy Problem for the Relativistic Boltzmann Equation with Near-Vacuum Data, Commun. Math. Phys., 264, 705-724, 2006.
  • 3. C. ECKART, The Thermodynamics of Irreversible Processes. III. Relativistic Theory of the Simple Fluid, Phys. Rev., 58, 919-924, 1940
  • 4. L.D. LANDAU, E.M. LIFSHITZ, Fluid Mechanics, Pergamon Press, Oxford 1959.
  • 5. W. ISRAEL, Relativistic Kinetic Theory of a Simple Gas, J. Math. Phys., 4, 1163, 1963.
  • 6. W. ISRAEL, J.M. STEWART, Thermodynamics of nonstationary and transient effects in a relativistic gas, Phys. Letters, 58A, 213-215, 1976.
  • 7. W. ISRAEL, J. M. STEWART, Transient relativistic thermodynamics and kinetic theory, Ann. Phys. (N.Y.), 118, 341-372, 1979.
  • 8. W. ISRAEL, J. M. STEWART, On Transient relativistic thermodynamics and kinetic theory. II, Proc. R. Soc. London, A 365, 43-52, 1979.
  • 9. I. SHIH Liu, I. MULLER and T. RUGGERI, Relativistic thermodynamics of gases, Ann. Phys., 169, 191-219, 1986.
  • 10. N. G. VAN KAMPEN, Chapman-Enskog as an application of the method for eliminating fast variables, J. Stat. Phys., 46, 709-727, 1987.
  • 11. U. HEINZ, Kinetic Theory for Plasmas with Non-Abelian Interactions, Phys. Rev. Lett., 51, 351-354, 1983.
  • 12. D. D. HOLM, B. A. KUPERSHMIDT, Relativistic chromohydrodynamics and Yang-Mills Vlasov plasma, Phys. Letters A, 105, 225-228, 1984.
  • 13. K. KAJANTIE, Hydrodynamics and approach to equilibrium in quark-gluon plasma, Nuclear Physics A, 418, 41-55, 1984.
  • 14. G. BAYM, [in:] Quark Matter '84, K. KAJANTIE [Ed.], Lecture Notes in Physics, Vol. 221, Springer, Berlin 1985.
  • 15. O. K. KALASHNIKOV, [in:] Quantum Field Theory and Quantum Statistics, [Ed.] I.A. Batalin et al., Vol. 1, p. 499, Adam Hilger, Bristol 1987.
  • 16. D. MIHALAS, B. W. MIHALAS, Foundations of radiation hydrodynamics, Oxford University Press, 1984.
  • 17. P. G. BERGMANN, Generalized statistical mechanics, Phys. Rev., 84, 1026-1033, 1951.
  • 18. P. HAVAS, [in:] Statistical mechanics of equilibrium and non-equilibrium, J. MEIXNER [Ed.], North Holland, Amsterdam 1965.
  • 19. J. L. SYNGE, The relativistic gas, North Holland, Amsterdam 1957.
  • 20. J. M. STEWART, Non-equilibrium relativistic kinetic theory. Lecture Notes in Physics, Vol. 10. Springer, Berlin 1971.
  • 21. S. R. DE GROOT, W. A. VAN LEEUWEN, CH. G. VAN WEERT, Non-Equilibrium relativistic kinetic theory-principles and applications. North Holland, Amsterdam 1980.
  • 22 M. DUDYŃSKI, M. L. EKIEL-JEŻEWSKA, On the linearized relativistic Boltzmann equation, Commun. Math. Phys., 115, 607, 1988.
  • 23. M. DUDYŃSKI, On the linearized relativistic Boltzmann equation. H. Existence of hydrodynamics, J. Stat. Phys., 57, 199, 1989.
  • 24. H. GRAD, Asymptotic theory of the Boltzmann equation, II, [in:] Third international rarefied gas symposium, J.A. LAUREMANN [Ed.], Academic Press, 1, p. 26, New York 1963.
  • 25. H. B. DRANGE, The linearized boltzmann collision operator for cut-off potentials, SIAM J. Appl. Math., 29, 665-676, 1975.
  • 26. R. S. ELLIS, M. A. PINSKY, The first and second fluid approximations to the linearized Boltzmann equation, J. Math. Pures et Appl., 54, 125-156, 1975, and The projection of the Navier-Stokes equations upon the Euler equations, J. Math. Pures et Appl., 54, 157-182, 1975.
  • 27. T. NISHIDA, Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation, Commun. Math. Phys., 61, 119-148, 1978.
  • 28. H. GRAD, [in:] Rarefied Gas Dynamics, F. M. DEVIENNE [Ed.], Pergamon Press, London 1960.
  • 29. L. D. LANDAU, E. M. LIFSHITZ, Quantum Mechanics-Non-Relativistic Theory, Part 1, Sec. 106 and 108, Pergamon Press, Oxford 1965.
  • 30. M. KLAUS, The linear Boltzmann operator-spectral properties and short-wavelength limit, Helv. Phys. Acta, 48, 99-129, 1975 and Boltzmann collision operator without cut-off, Helv. Phys. Acta, 50, 893-903, 1977.
  • 31. YOUNG-PING PAO, Boltzmann collision operator with inverse-power intermolecular potentials, I, Comm. Pure Appl. Math., 27, 407—428, and Boltzmann collision operator with inverse-power intermolecular potentials, II Comm. Pure Appl. Math., 559-581, 1974.
  • 32. G. SIACOMELLI, Total cross sections and elastic scattering at high energies, Phys. Reports, 23, 123-235, 1976.
  • 33. B.H. BRANSDEN, D. EVANS, J.V. MAJOR, The fundamental particles, Van Nostrand Reinhold Company, London 1973.
  • 34. M. DUDYŃSKI, M.L. EKIEL-JEŻEWSKA, Causality of the linearized relativistic Boltzmann equation, Phys. Rev. Lett., 55, 2831-2834, 1985.
  • 35. M. DUDYŃSKI, M.L. EKIEL-JEŻEWSKA, Causality problem in the relativistic kinetic theory, [in:] Recent developments in nonequilibrium thermodynamics: Fluids and related topics, J. CASAS—VÁZQUEZ et. al. [Ed.], Lecture Notes in Physics, Vol. 253. Springer, Berlin 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0014-0038
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.