Analysis of a coupled system of kinetic equations and conservation laws: Rigorous derivation and existence theory via defect measures

Tidriri, M.

doi:10.1090/S0002-9947-05-03830-4

Analysis of a coupled system of kinetic equations and conservation laws: Rigorous derivation and existence theory via defect measures
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Abstract:

In this paper we introduce a coupled system of kinetic equations of B.G.K. type and then study its hydrodynamic limit. We obtain as a consequence the rigorous derivation and existence theory for a coupled system of kinetic equations and their hydrodynamic (conservation laws) limit. The latter is a particular case of the coupled system of Boltzmann and Euler equations. A fundamental element in this study is the rigorous derivation and justification of the interface conditions between the kinetic model and its hydrodynamic conservation laws limit, which is obtained using a new regularity theory introduced herein.

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Tidriri M. D., Analysis of a coupled system of kinetic equations and their hydrodynamic (conservation laws) limit: rigorous derivation and existence theory via BV theory. Accepted.
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Tidriri M., Hydrodynamic limit of a B.G.K. kinetic model and kinetic formulation of conservation laws on domains with boundaries. To appear in Archive for Rational Mechanics and Analysis.