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Caflisch, Russel E.; Papanicolaou, George C.

The fluid-dynamical limit of a nonlinear model Boltzmann equation. (English) Zbl 0438.76059

Commun. Pure Appl. Math. 32, 589-616 (1979).
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Cited in 1 Review
Cited in 42 Documents

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics

Keywords:

Boltzmann equation; fluid dynamical limit; Broadwell’s model; discrete- velocity gas; one dimension; fluid-dynamical approximation; asymptotic expansion; Hilbert expansion; existence and uniqueness; local Maxwellian
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\textit{R. E. Caflisch} and \textit{G. C. Papanicolaou}, Commun. Pure Appl. Math. 32, 589--616 (1979; Zbl 0438.76059)
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References:

[1] Broadwell, Phys. Fluids 7 pp 1243– (1964)
[2] Godunov, Uspehi Mat. Nauk. 26 pp 3– (1971)
[3] Grad, Handb. Phys. 12 pp 205– (1958)
[4] Grad, Phys. Fluids 6 pp 147– (1963)
[5] Asymptotic equivalence of the Navier-Stokes and nonlinear Boltzmann equations, Proc. Symp. Appl. XVII Applications of Nonlinear PDE in Math. Phys., 1965, Providence, R.I., pp. 154–183.
[6] Singular and nonuniform limits of solutions of the Boltzmann equation, SIAM-AMS Proceedings, I., Transport Theory, 1969, Providence, R. I., pp. 296–308.
[7] Fluid dynamical limit of the nonlinear Boltzmann equation in the level of the compressible Euler equations, to appear.
[8] Inoue, Appl. Math. Optin. 3 pp 27– (1976)
[9] Kurtz, Trans. Amer. Math. Soc. 186 pp 259– (1973)
[10] McKean, Israel J. Math. 21 pp 54– (1975)
[11] Boltzmann and Navier-Stokes shock profiles for the Broadwell model, to appear.
[12] Lax, Comm. Pure Appl. Math. 10 pp 575– (1957)
[13] and , Methods of Mathematical Physics, Vol. II, Interscience, New York, 1962.
[14] and , The Mathematical Theory of Non-Uniform Gases, Cambridge, 1939. · Zbl 0063.00782
[15] Grundzüge einer Allgemeinen Theorie der Linearen Integralgleichungen, Teubner, 1912.
[16] Kinetische Theorie der Vorgänge in Mässig Verdünnten Gasen, Uppsala, 1917.
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