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The fluid‐dynamical limit of a nonlinear model boltzmann equation

1979; Wiley; Volume: 32; Issue: 5 Linguagem: Inglês

10.1002/cpa.3160320502

1097-0312

Russel E. Caflisch, George Papanicolaou,

Fluid Dynamics and Turbulent Flows

Communications on Pure and Applied MathematicsVolume 32, Issue 5 p. 589-616 Article The fluid-dynamical limit of a nonlinear model boltzmann equation Russel E. Caflisch, Russel E. CaflischSearch for more papers by this authorGeorge C. Papanicolaou, George C. PapanicolaouSearch for more papers by this author Russel E. Caflisch, Russel E. CaflischSearch for more papers by this authorGeorge C. Papanicolaou, George C. PapanicolaouSearch for more papers by this author First published: September 1979 https://doi.org/10.1002/cpa.3160320502Citations: 69AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Bibliography 1 Broadwell, J. E., Shock structure in a simple discrete velocity gas, Phys. Fluids 7, 1964, pp. 1243– 1247. 2 Godunov, S. K., and Sultangazin, U. M., On discrete models of the kinetic Boltzmann equation, Uspehi Mat. Nauk. 26, 1971, pp. 3– 51. 3 Grad, H., Principles of the kinetic theory of gases, Handb. Phys. 12, 1958, pp. 205– 294. 4 Grad, H., Asymptotic theory of the Boltzmann equation, Phys. Fluids 6, 1963, pp. 147– 181. 5 Grad, H., 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 Grad, H., Singular and nonuniform limits of solutions of the Boltzmann equation, SIAM-AMS Proceedings, I., Transport Theory, 1969, Providence, R. I., pp. 296– 308. 7 Nishida, T., Fluid dynamical limit of the nonlinear Boltzmann equation in the level of the compressible Euler equations, to appear. 8 Inoue, K., and Nishida, T., On the Broadwell model of the Boltzmann equation for a simple discrete velocity gas, Appl. Math. Optin. 3, 1976, pp. 27– 49. 9 Kurtz, T. G., Convergence of sequences of semi-groups of nonlinear operators with an application to gas kinetics, Trans. Amer. Math. Soc. 186, 1973, pp. 259– 272. 10 McKean, H. P., The central limit theorem for Carleman's equation, Israel J. Math. 21, 1975, pp. 54– 92. 11 Caflisch, R., Boltzmann and Navier-Stokes shock profiles for the Broadwell model, to appear. 12 Lax, P. D., Hyperbolic systems of conservation laws, II, Comm. Pure Appl. Math. 10, 1957, pp. 575– 566. 13 Courant, R., and Hilbert, D., Methods of Mathematical Physics, Vol. II, Interscience, New York, 1962. 14 Chapman, S., and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, Cambridge, 1939. 15 Hilbert, D., Grundzüge einer Allgemeinen Theorie der Linearen Integralgleichungen, Teubner, 1912. 16 Enskog, D., Kinetische Theorie der Vorgänge in Mässig Verdünnten Gasen, Uppsala, 1917. Citing Literature Volume32, Issue5September 1979Pages 589-616 ReferencesRelatedInformation