Hamiltonian and Godunov structures of the Grad hierarchy
Status PubMed-not-MEDLINE Language English Country United States Media print-electronic
Document type Journal Article
- Publication type
- Journal Article MeSH
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
Zhou Pei Yuan Center for Applied Mathematics Tsinghua University Beijing China
References provided by Crossref.org
Gradient and GENERIC time evolution towards reduced dynamics
Thermodynamic Explanation of Landau Damping by Reduction to Hydrodynamics
