Small velocity and finite temperature variations in kinetic relaxation models

Kazuo Aoki*, Ansgar Jüngel, Peter A. Markowich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A small Knuden number analysis of a kinetic equation in the diffusive scaling is performed. The collision kernel is of BGK type with a general local Gibbs state. Assuming that the flow velocity is of the order of the Knudsen number, a Hilbert expansion yields a macroscopic model with finite temperature variations, whose complexity lies in between the hydrodynamic and the energy-transport equations. Its mathematical structure is explored and macroscopic models for specific examples of the global Gibbs state are presented.

Original languageEnglish (US)
Pages (from-to)1-15
Number of pages15
JournalKinetic and Related Models
Issue number1
StatePublished - Mar 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-I1-007-43
Acknowledgements: The work of the first author is supported by the Grant-in-Aid for Scientific Research No. 20360046 from the Japanese Society for the Promotion of Science (JSPS). The second author acknowledges partial support from the Austrian Science Fund (FWF), grant P20214 and WK "Differential Equations", the German Science Foundation (DFG), grant JU 359/7, and the Austrian-Croatian Project of the Austrian Exchange Service (OAD). Part of this research was carried out during the stay of the second author at the institute of the first author; support by the exchange program of the Austrian BMWF and the Japanese JSPS is acknowledged. The work of the last author is supported by Award No. KUK-I1-007-43, funded by the King Abdullah University of Science and Technology (KAUST), and by his Royal Society Wolfson Research Merit Award.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


  • Diffusive limit
  • Energy-transport equations
  • Gibbs state
  • Hydrodynamic equations
  • Kinetic equation

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation


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