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A discrete velocity model of a gas: Global in time solutions of the BBGKY hierarchy |
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| Authors: | G. Borgioli V. Gerasimenko G. Lauro R. Monaco |
| Affiliation: | Dipartimento di Ingegneria Elettronica, Università di Firenze, via S. Marta 3, 50139 Firenze, Italy;Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivs'ka Str. 3, 252004 Kyiv, Ukraine;Dipartimento di Matematica Applicata “G. Sansone”, Università di Firenze, via S. Marta 3, 50139 Firenze, Italy;Dipartimento di Matematica, Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italy |
| Abstract: | In the present paper we study the evolution of a system of hard disks moving in the plane with a finite number of velocities as in the framework of a discrete velocity model of the Enskog equation, proposed in previous papers. Starting from the BBGKY hierarchy of such a system we give existence and uniqueness results for the initial value problem in suitable Banach spaces. In particular, the main result presented is the global in time weak solution to the BBGKY hierarchy for local equilibrium initial data, in the thermodynamic limit. |
| Keywords: | discrete velocity kinetic models many particles dynamical systems BBGKY hierarchies Enskog equation semigroups of operators evolution equations existence and uniqueness to the Cauchy problem |
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