A kinetic model for polytropic gases with internal energy. Issue 1 (29th November 2013)

• Record Type: Journal Article
• Authors: Boudin, Laurent; Grec, Bérénice; Pavić‐Čolić, Milana; Salvarani, Francesco
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 13:Issue 1(2013)
• Page Start: 353
• Page End: 354
• Publication Date: 2013-11-29
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201310172
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function f i (t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on${\rm I\!R}_+\times{\rm I\!R}^3\times{\rm I\!R}^3\times{\rm I\!R}_+$, and its evolution is governed by a Boltzmann‐type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L 1 space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L 2 framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)