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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Asymptotic nonuniqueness of the Navier-Stokes equations in kinetic theory


Authors: Richard S. Ellis and Mark A. Pinsky
Journal: Bull. Amer. Math. Soc. 80 (1974), 1160-1164
MSC (1970): Primary 82A40, 76D30; Secondary 15A27, 76Q05, 45M05
MathSciNet review: 0609539
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  • 1. Richard S. Ellis and Mark A. Pinsky, Limit theorems for model Boltzmann equations with several conserved quantities, Indiana Univ. Math. J. 23 (1973), 287–307. MR 0319514 (47 #8058)
  • 2. Richard S. Ellis and Mark A. Pinsky, Asymptotic equivalence of the linear Navier-Stokes and heat equations in one dimension, J. Differential Equations 17 (1975), 406–420. MR 0609546 (58 #29431)
  • 3. Richard S. Ellis and Mark A. Pinsky, The projection of the Navier-Stokes equations upon the Euler equations, J. Math. Pures Appl. (9) 54 (1975), 157–181. MR 0609545 (58 #29430c)
  • 4. R. Ellis and M. Pinsky, The first and second fluid approximations to the Boltzmann equation, J. Math. Pures Appl. (to appear).
  • 5. J. D. Foch and G. W. Ford, The dispersion of sound in monoatomic cases, Studies in Statistical Mechanics, vol. 5, North-Holland, Amsterdam, 1970.
  • 6. Harold Grad, Asymptotic theory of the Boltzmann equation. II, Rarefied Gas Dynamics (Proc. 3rd Internat. Sympos., Palais de l’UNESCO, Paris, 1962) Academic Press, New York, 1963, pp. 26–59. MR 0156656 (27 #6577)
  • 7. Harold Grad, Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Sympos. Appl. Math., Vol. XVII, Amer. Math. Soc., Providence, R.I., 1965, pp. 154–183. MR 0184507 (32 #1979)
  • 8. Harold Grad, Solution of the Boltzmann equation in an unbounded domain, Comm. Pure Appl. Math. 18 (1965), 345–354. MR 0191508 (32 #8913)
  • 9. Tosio Kato, Perturbation theory for linear operators, Die Grundlehren der mathematischen Wissenschaften, Band 132, Springer-Verlag New York, Inc., New York, 1966. MR 0203473 (34 #3324)
  • 10. James A. McLennan, Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation, Phys. Fluids 8 (1965), 1580–1584. MR 0198794 (33 #6948)
  • 11. B. Nicolaenko, Dispersion laws for plane wave propagation, The Boltzmann Equation (ed. by F. A. Grünbaum), Courant Institute of Mathematical Sciences, New York, 1971, pp. 125-173.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1974-13656-6
PII: S 0002-9904(1974)13656-6