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On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation. (English) Zbl 0449.76053

MSC:
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
35K05 Heat equation
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[1] Chapman, S., Cowling, T.: The mathematical theory of non-uniform gases, 3rd ed. London: Cambridge University Press 1970 · Zbl 0063.00782
[2] Ellis, R., Pinsky, M.: The first and second fluid approximations to the linearized Boltzmann equation. J. Math. Pures Appl.54, 125–156 (1975) · Zbl 0286.35062
[3] Ellis, R., Pinsky, M.: The projection of the Navier-Stokes equations upon the Euler equations. J. Math. Pures Appl.54, 157–181 (1975) · Zbl 0286.35063
[4] Grad, H.: Asymptotic theory of the Boltzmann equation. Phys. Fluids6, 147–181 (1963) · Zbl 0115.45006 · doi:10.1063/1.1706716
[5] Grad, H.: Asymptotic theory of the Boltzmann equation. II. In: Rarefied gas dynamics, Vol. 1 (ed. J. Laurmann), pp. 26–59. New York: Academic Press 1963
[6] Grad, H.: Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations. Proc. Symp. Appl. Math., Am. Math. Soc.17, 154–183 (1965) · Zbl 0144.48203
[7] Kawashima, S.: The asymptotic equivalence of the Broadwell model equation and its Navier-Stokes model equation (to appear) · Zbl 0477.76034
[8] Leray, J.: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math.63, 193–248 (1934) · JFM 60.0726.05 · doi:10.1007/BF02547354
[9] Matsumura, A., Nishida, T.: The initial value problem for the equations of motion of viscous and heat-conductive gases. J. Math. Kyoto Univ. (in press) · Zbl 0429.76040
[10] Matsumara, A., Nishida, T.: The initial value problem for the equations of motion of compressible, viscous and heat-conductive fluids. II (to appear in Proc. Jpn. Acad.)
[11] McLennan, J.: Convergence of the Chapman-Enskog expansion for the linearized Boltzmann equation. Phys. Fluids8, 1580–1584 (1965) · doi:10.1063/1.1761467
[12] Nishida, T.: Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation. Commun. Math. Phys.61, 119–148 (1978) · Zbl 0381.76060 · doi:10.1007/BF01609490
[13] Nishida, T., Imai, K.: Global solutions to the initial value problem for the nonlinear Boltzmann equation. Publ. Res. Inst. Math. Sci., Kyoto Univ.12, 229–239 (1976) · Zbl 0344.35003 · doi:10.2977/prims/1195190965
[14] Pinsky, M.: On the Navier-Stokes approximation to the linearized Boltzmann equation. J. Math. Pures Appl.55, 217–231 (1976) · Zbl 0296.35057
[15] Ukai, S.: Les solutions globales de l’équation nonlinéaire de Boltzmann dans l’espace tout entier et dans le demi-espace. Compte Rendu Acad. Sci. Paris282 A, 317–320 (1976) · Zbl 0345.45012
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