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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited 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 PDF BibTeX XML Cite \textit{R. E. Caflisch} and \textit{G. C. Papanicolaou}, Commun. Pure Appl. Math. 32, 589--616 (1979; Zbl 0438.76059) Full Text: DOI OpenURL 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. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.