The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of gradient dynamics guaranteeing the growth of entropy and consequently the approach to equilibrium. We carry all three structures to the Grad reformulation of the Boltzmann equation (to the Grad hierarchy). First, we recognize the structures in the infinite Grad hierarchy and then in several examples of finite hierarchies representing extended hydrodynamic equations. In the context of Grad's hierarchies, we also investigate relations between Hamiltonian and Godunov structures.

Departament de Fisica Universitat Autonoma de Barcelona 08193 Bellaterra Catalonia Spain

École Polytechnique de Montréal C P 6079 Succ Centre ville Montréal Québec Canada H3C 3A7

Mathematical Institute Faculty of Mathematics Charles University Prague Sokolovská 83 18675 Prague Czech Republic

Thermodynamique des Phénomènes Irréversibles Université de Liège Quartier Agora Allée 6 Août 19 4000 Liège Belgique

Zhou Pei Yuan Center for Applied Mathematics Tsinghua University Beijing China

Citace poskytuje Crossref.org

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