Hydrodynamic limits of Vlasov-Fokker-Planck equation for granular media
Benedetto, Dario ; Caglioti, Emanuele ; Golse, François ; Pulvirenti, Mario
Commun. Math. Sci., Tome 2 (2004) no. 2, p. 121-136 / Harvested from Project Euclid
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This paper, which is a sequel to Benedetto-Caglioti-Golse-Pulvirenti, Comput. Math. Appl. 38 (1999), p. 121-131, considers as a starting point a mean-field equation for the dynamics of a gas of particles interacting via dissipative binary collisions. More precisely, we are concerned with the case where these particles are immersed in a thermal bath modeled by a linear Fokker-Planck operator. Two different scalings are considered for the resulting equation. One concerns the case of a thermal bath at finite temperature and leads formally to a nonlinear diffusion equation. The other concerns the case of a thermal bath at infinite temperature and leads formally to an isentropic Navier-Stokes system. Both formal limits rest on the mathematical properties of the linearized mean-field operator which are established rigorously, and on a Hilbert or Chapman-Enskog expansion.
Publié le : 2004-03-15
Classification:  Granular media,  Vlasov-Fokker-Planck equation,  hydrodynamic limits,  HIlbert expansion,  Chapman-Enskog expansion,  82C40,  76T25,  76M45 
@article{1250880212,
     author = {Benedetto, Dario and Caglioti, Emanuele and Golse, Fran\c cois and Pulvirenti, Mario},
     title = {Hydrodynamic limits of Vlasov-Fokker-Planck equation for granular media},
     journal = {Commun. Math. Sci.},
     volume = {2},
     number = {2},
     year = {2004},
     pages = { 121-136},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250880212}
}

Benedetto, Dario; Caglioti, Emanuele; Golse, François; Pulvirenti, Mario. Hydrodynamic limits of Vlasov-Fokker-Planck equation for granular media. Commun. Math. Sci., Tome 2 (2004) no. 2, pp.  121-136. http://gdmltest.u-ga.fr/item/1250880212/