Boudin, Laurent; Grec, Bérénice; Salvarani, Francesco The Maxwell-Stefan diffusion limit for a kinetic model of mixtures. (English) Zbl 1320.35250 Acta Appl. Math. 136, No. 1, 79-90 (2015). Summary: We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit. Cited in 23 Documents MSC: 35Q20 Boltzmann equations 35B25 Singular perturbations in context of PDEs Keywords:diffusion limit; Maxwell-Stefan equations; Boltzmann equations; gaseous mixture PDFBibTeX XMLCite \textit{L. Boudin} et al., Acta Appl. Math. 136, No. 1, 79--90 (2015; Zbl 1320.35250) Full Text: DOI HAL References: [1] Andries, P., Aoki, K., Perthame, B.: A consistent BGK-type model for gas mixtures. J. Stat. Phys. 106(5-6), 993-1018 (2002) · Zbl 1001.82093 [2] Bardos, C., Golse, F., Levermore, C.D.: Sur les limites asymptotiques de la théorie cinétique conduisant à la dynamique des fluides incompressibles. C. R. Acad. Sci., Sér. 1 Math. 309(11), 727-732 (1989) · Zbl 0697.35111 [3] Bardos, C., Golse, F., Levermore, C.D.: Fluid dynamic limits of kinetic equations. I. Formal derivations. J. Stat. Phys. 63(1-2), 323-344 (1991) [4] Bardos, C., Golse, F., Levermore, C.D.: Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Commun. Pure Appl. Math. 46(5), 667-753 (1993) · Zbl 0817.76002 [5] Bisi, M., Desvillettes, L.: Formal passage from kinetic theory to incompressible Navier-Stokes equations for a mixture of gases. Modél. Math. Anal. Numér. (2014, to appear). doi:10.1051/m2an/2013135 · Zbl 1301.82046 [6] Bothe, D., On the Maxwell-Stefan approach to multicomponent diffusion, No. 80, 81-93 (2011), Basel · Zbl 1250.35127 [7] Boudin, L.; Götz, D.; Grec, B., Diffusion models of multicomponent mixtures in the lung, No. 30, 90-103 (2010), Les Ulis · Zbl 1202.76106 [8] Boudin, L., Grec, B., Pavić, M., Salvarani, F.: Diffusion asymptotics of a kinetic model for gaseous mixtures. Kinet. Relat. Models 6(1), 137-157 (2013) · Zbl 1260.35100 [9] Boudin, L., Grec, B., Salvarani, F.: A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations. Discrete Contin. Dyn. Syst., Ser. B 17(5), 1427-1440 (2012) · Zbl 1245.35091 [10] Brull, S., Pavan, V., Schneider, J.: Derivation of a BGK model for mixtures. Eur. J. Mech. B, Fluids 33, 74-86 (2012) · Zbl 1258.76122 [11] Chang, H.K.: Multicomponent diffusion in the lung. Fed. Proc. 39(10), 2759-2764 (1980) [12] Desvillettes, L., Monaco, R., Salvarani, F.: A kinetic model allowing to obtain the energy law of polytropic gases in the presence of chemical reactions. Eur. J. Mech. B, Fluids 24(2), 219-236 (2005) · Zbl 1060.76100 [13] Duncan, J.B., Toor, H.L.: An experimental study of three component gas diffusion. AIChE J. 8(1), 38-41 (1962) [14] Garzó, V., Santos, A., Brey, J.J.: A kinetic model for a multicomponent gas. Phys. Fluids A 1(2), 380-383 (1989) · Zbl 0661.76080 [15] Giovangigli, V., Multicomponent flow modeling (1999), Cambridge · Zbl 0956.76003 [16] Golse, F., Saint-Raymond, L.: The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels. Invent. Math. 155(1), 81-161 (2004) · Zbl 1060.76101 [17] Golse, F., Saint-Raymond, L.: The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials. J. Math. Pures Appl. (9) 91(5), 508-552 (2009) · Zbl 1178.35290 [18] Hilbert, D.: Mathematical problems. Bull. Am. Math. Soc. 8(10), 437-479 (1902) · JFM 33.0976.07 [19] Jüngel, A., Stelzer, I.V.: Existence analysis of Maxwell-Stefan systems for multicomponent mixtures. SIAM J. Math. Anal. 45(4), 2421-2440 (2013) · Zbl 1276.35104 [20] Krishna, R., Wesselingh, J.A.: The Maxwell-Stefan approach to mass transfer. Chem. Eng. Sci. 52(6), 861-911 (1997) [21] Maxwell, J.C.: On the dynamical theory of gases. Philos. Trans. R. Soc. Lond. 157, 49-88 (1866) [22] Morse, T.F.: Kinetic model equations for a gas mixture. Phys. Fluids 7, 2012-2013 (1964) [23] Shigesada, N., Kawasaki, K., Teramoto, E.: Spatial segregation of interacting species. J. Theor. Biol. 79(1), 83-99 (1979) [24] Sirovich, L.: Kinetic modeling of gas mixtures. Phys. Fluids 5, 908-918 (1962) · Zbl 0118.23602 [25] Stefan, J.: Ueber das Gleichgewicht und die Bewegung insbesondere die Diffusion von Gasgemengen. Akad. Wiss. Wien 63, 63-124 (1871) [26] Thiriet, M., Douguet, D., Bonnet, J.-C., Canonne, C., Hatzfeld, C.: The effect on gas mixing of a He-O2 mixture in chronic obstructive lung diseases. Bull. Eur. Physiopathol. Respir. 15(5), 1053-1068 (1979). In French [27] Williams, F.A.: Combustion Theory, 2nd edn. Benjamin-Cummings, Redwood City (1985) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.