The acoustic limit for the Boltzmann equation

Archive for Rational Mechanics and Analysis

Volumn 153, Issue 3, 2000, Pages 177-204

  Bardos, Claude ^a   Golse, François ^a   Levermore, C David ^a  

^a Inserm   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034391961     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050000080     Document Type: Article

References (27)

1. C. BARDOS, F. GOLSE, & D. LEVERMORE, Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles, C.R. Acad. Sci. Paris 309, (1989) 727-732.
2. C. BARDOS, F. GOLSE, & D. LEVERMORE, Fluid Dynamic Limits of Kinetic Equations I: Formal Derivations, J. Stat. Phys. 63, (1991) 323-344.
3. C. BARDOS, F. GOLSE, & C. D. LEVERMORE, Fluid Dynamic Limits of Kinetic Equations II: Convergence Proofs for the Boltzmann Equation, Commun. Pure & Appl. Math. 46, (1993) 667-753.
4. C. BARDOS, F. GOLSE, & C. D. LEVERMORE, Acoustic and Stokes Limits for the Boltzmann Equation, C.R. Acad. Sci. Paris 327, (1999) 323-328.
5. C. BARDOS, F. GOLSE, & C. D. LEVERMORE, The Stokes Limit for the Boltzmann Equation, preprint.
6. C. BARDOS & C. D. LEVERMORE, Kinetic Equations and an Incompressible Fluid Dynamical Limit that Recovers Viscous Heating, (in preparation 1999).
7. C. BARDOS & S. UKAI, The Classical Incompressible Navier-Stokes Limit of the Boltzmann Equation, Math. Models & Meth. Appl. Sci. 1, (1991) 235-257.
8. A. V. BOBYLEV, Quasistationary Hydrodynamics for the Boltzmann Equation, J. Stat. Phys. 80, (1995) 1063-1083.
9. F. BOUCHUT, F. GOLSE, AND M. PULVIRENTI, Kinetic Equations and Asymptotic Theories, L. DESVILLETTES & B. PERTHAME eds., (Gauthier-Villars Elsevier, Paris 1999).
10. L. BOLTZMANN, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen Sitzungs. Akad. Wiss. Wien 66, (1872) 275-370; English translation in Kinetic Theory, vol. 2 S.G. BRUSH ed. (Pergamon Press, London 1966) 88-174.
11. L. BOLTZMANN, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen Sitzungs. Akad. Wiss. Wien 66, (1872) 275-370; English translation in Kinetic Theory, vol. 2 S.G. BRUSH ed. (Pergamon Press, London 1966) 88-174.
12. R. CAFLISCH, The Fluid Dynamical Limit of the Nonlinear Boltzmann Equation, Commun. Pure & Appl. Math. 33, (1980) 651-666.
13. C. CERCIGNANI, The Boltzmann Equation and its Applications, (Springer-Verlag, New York 1988).
14. C. CERCIGNANI, R. ILLNER, & M. PULVIRENTI, The Mathematical Theory of Dilute Gases, (Springer-Verlag, New York 1994).
15. A. DEMASI, R. ESPOSITO, AND J. LEBOWITZ, Incompressible Navier-Stokes and Euler Limits of the Boltzmann Equation, Commun. Pure & Appl. Math. 42, (1990) 1189-1214.
16. R. J. DIPERNA & P.-L. LIONS, On the Cauchy Problem for the Boltzmann Equation: Global Existence and Weak Stability Results, Annals of Math. 130, (1990) 321-366.
17. D. ENSKOG, Kinetische Theorie der Vorgänge in mässig verdünnten Gasen, I. Allgemeiner Teil, Uppsala, Almqvist & Wiksell; English translation in Kinetic Theory, vol. 3 S. G. BRUSH ed. (Pergamon Press, Oxford 1972) 125-225.
18. D. ENSKOG, Kinetische Theorie der Vorgänge in mässig verdünnten Gasen, I. Allgemeiner Teil, Uppsala, Almqvist & Wiksell; English translation in Kinetic Theory, vol. 3 S. G. BRUSH ed. (Pergamon Press, Oxford 1972) 125-225.
19. H. GRAD, Principles of the Kinetic Theory of Gases, Handbuch der Physik vol. 12 S. FLÜGGE ed. (Springer-Verlag, Berlin 1958) 205-294.
20. D. HILBERT, Begründung der kinetischen Gastheorie, Math. Annalen 72, (1912) 562-577; English translation in Kinetic Theory, vol. 3 S. G. BRUSH ed. (Pergamon Press, Oxford 1972) 89-101.
21. D. HILBERT, Begründung der kinetischen Gastheorie, Math. Annalen 72, (1912) 562-577; English translation in Kinetic Theory, vol. 3 S. G. BRUSH ed. (Pergamon Press, Oxford 1972) 89-101.
22. C. D. LEVERMORE, Entropic Convergence and the Linearized Limit for the Boltzmann Equation, Commun. P.D.E. 18, (1993) 1231-1248.
23. P.-L. LIONS, Mathematical Topics in Fluid Mechanics, Vol. I: Incompressible Models, (Oxford University Press, New York 1996)
24. J. C. MAXWELL, On the Dynamical Theory of Gases, Phil. Trans. Roy. Soc. London 157, (1866) 49-88.
25. T. SIDERIS, Formation of Singularities in Three Dimensional Compressible Fluids, Commun. Math. Phys. 101, (1985) 475-485.
26. Y. SONE, Asymptotic Theory of a Steady Flow of Rarefied Gas Past Bodies for Small Knudsen Numbers, in Advances in Kinetic Theory and Continuum Mechanics, R. GATIGNOL & SOUBBARAMAYER eds. (Springer-Verlag, Berlin 1991) 19-31.
27. S. UKAI, The Incompressible Limit and the Initial Layer of the Compressible Euler Equation, J. Math. Kyoto Univ. 26, (1986) 323-331.