Small velocity and finite temperature variations in kinetic relaxation models

Handle URI:
http://hdl.handle.net/10754/599648
Title:
Small velocity and finite temperature variations in kinetic relaxation models
Authors:
Markowich, Peter; Jüngel, Ansgar; Aoki, Kazuo
Abstract:
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. © American Institute of Mathematical Sciences.
Citation:
Markowich P, Jüngel A, Aoki K (2010) Small velocity and finite temperature variations in kinetic relaxation models. KRM 3: 1–15. Available: http://dx.doi.org/10.3934/krm.2010.3.1.
Publisher:
American Institute of Mathematical Sciences (AIMS)
Journal:
Kinetic and Related Models
KAUST Grant Number:
KUK-I1-007-43
Issue Date:
Jan-2010
DOI:
10.3934/krm.2010.3.1
Type:
Article
ISSN:
1937-5093
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorMarkowich, Peteren
dc.contributor.authorJüngel, Ansgaren
dc.contributor.authorAoki, Kazuoen
dc.date.accessioned2016-02-28T06:06:39Zen
dc.date.available2016-02-28T06:06:39Zen
dc.date.issued2010-01en
dc.identifier.citationMarkowich P, Jüngel A, Aoki K (2010) Small velocity and finite temperature variations in kinetic relaxation models. KRM 3: 1–15. Available: http://dx.doi.org/10.3934/krm.2010.3.1.en
dc.identifier.issn1937-5093en
dc.identifier.doi10.3934/krm.2010.3.1en
dc.identifier.urihttp://hdl.handle.net/10754/599648en
dc.description.abstractA 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. © American Institute of Mathematical Sciences.en
dc.description.sponsorshipThe 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.en
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)en
dc.subjectDiffusive limiten
dc.subjectEnergy-transport equationsen
dc.subjectGibbs stateen
dc.subjectHydrodynamic equationsen
dc.subjectKinetic equationen
dc.titleSmall velocity and finite temperature variations in kinetic relaxation modelsen
dc.typeArticleen
dc.identifier.journalKinetic and Related Modelsen
dc.contributor.institutionKyoto University, Kyoto, Japanen
dc.contributor.institutionTechnische Universitat Wien, Vienna, Austriaen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
kaust.grant.numberKUK-I1-007-43en
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