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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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  • 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
  • 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
  • 4. R. Ellis and M. Pinsky, The first and second fluid approximations to the Boltzmann equation, J. Math. Pures Appl. (to appear).
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  • 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
  • 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
  • 8. Harold Grad, Solution of the Boltzmann equation in an unbounded domain, Comm. Pure Appl. Math. 18 (1965), 345–354. MR 0191508
  • 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
  • 10. James A. McLennan, Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation, Phys. Fluids 8 (1965), 1580–1584. MR 0198794
  • 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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DOI: http://dx.doi.org/10.1090/S0002-9904-1974-13656-6