Benedetto, D.; Caglioti, E.; Golse, F.; Pulvirenti, M. A hydrodynamic model arising in the context of granular media. (English) Zbl 0946.76096 Comput. Math. Appl. 38, No. 7-8, 121-131 (1999). Summary: We propose a formal argument identifying the hydrodynamic limit of a Fokker-Planck model for granular media. More precisely, in the limit of large background temperature and vanishing friction, this hydrodynamic limit is described by the classical system of isentropic gas dynamics with a nonstandard pressure law (specifically, the pressure is proportional to the cube root of the density). Finally, some qualitative properties of the hydrodynamic model are studied. Cited in 8 Documents MSC: 76T25 Granular flows 74E20 Granularity Keywords:inelastic particle system; hydrodynamic limit; Fokker-Planck model; granular media; isentropic gas dynamics; nonstandard pressure law PDFBibTeX XMLCite \textit{D. Benedetto} et al., Comput. Math. Appl. 38, No. 7--8, 121--131 (1999; Zbl 0946.76096) Full Text: DOI References: [1] Benedetto, D.; Caglioti, E.; Carrillo, J.; Pulvirenti, M., A non-Maxwellian steady distribution for one-dimensional granular media, J. of Stat. Phys., 91, 5/6, 979-990 (1998) · Zbl 0921.60057 [2] McNamara, S.; Young, W. R., Kinetic of a 1-dimensional medium in the quasi-elastic limit, Phys. of Fluids A, 7, 3, 34-45 (1995) [3] Du, Y.; Li, H.; Kadanoff, L., Breakdown of hydrodynamics in a 1-dimensional system of inelastic particles, Phys. Rev. Lett., 74, 8, 1268-1271 (1995) [4] Benedetto, D.; Caglioti, E.; Pulvirenti, M., A kinetic equation for granular media, RAIRO Modél. Math. Anal. Numér., 31, 5, 615-641 (1997) · Zbl 0888.73006 [5] Puglisi, A.; Loreto, V.; Marini Bettolo Marconi, U.; Petri, A.; Vulpiani, A., Clustering and non-Gaussian behavior in granular matter, Phys. Rev. Lett., 81, 3848 (1998) [6] Lions, P.-L., Mathematical Topics in Fluid Mechanics, Vol. 2: Compressible Models (1998), Clarendon Press: Clarendon Press Oxford · Zbl 0908.76004 [7] Grenier, E., Existence globale pour el système de gaz sans pression, C. R. Acad. Sci. Paris Sér. I Math., 431, 2, 171-174 (1995) · Zbl 0837.35088 [8] Bouchut, F.; James, F., Duality solutions for pressureless gases, monotone scalar conservation laws and uniqueness (1998), Preprint [9] Smoller, J., Shock Waves and Reaction Diffusion Equations (1983), Springer-Verlag: Springer-Verlag Berlin · Zbl 0508.35002 [10] Chorin, A. J.; Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (1979), Springer-Verlag: Springer-Verlag New York · Zbl 0417.76002 [11] Saint-Raymond, L., Approximation isentropique du système d’Euler compressible en dimension 1, C. R. Acad. Sci., 327, 613-616 (1998), (Série I) · Zbl 1040.76515 [12] Cercignani, C.; Illner, R.; Pulvirenti, M., The mathematical theory of dilute gases, (Applied Mathematical Sciences, Vol. 106 (1994), Springer-Verlag: Springer-Verlag New York) · Zbl 0813.76001 [13] Constantin, P.; Grossman, E.; Mungan, M., Inelastic collisions of 3 particles on the line as a 2-dimensional billiards, Physica D, 83, 409-420 (1995) · Zbl 0900.70198 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.