From gas dynamics with large friction to gradient flows describing diffusion theories

Handle URI:
http://hdl.handle.net/10754/603947
Title:
From gas dynamics with large friction to gradient flows describing diffusion theories
Authors:
Lattanzio, Corrado; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
We study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Informa UK Limited
Journal:
Communications in Partial Differential Equations
Issue Date:
9-Dec-2016
DOI:
10.1080/03605302.2016.1269808
ARXIV:
1601.05966
Type:
Article
Sponsors:
AET was supported by funding from King Abdullah University of Science and Technology (KAUST).
Additional Links:
http://arxiv.org/abs/1601.05966
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorLattanzio, Corradoen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2016-12-13T07:31:20Z-
dc.date.available2016-03-30T07:34:04Zen
dc.date.available2016-12-13T07:31:20Z-
dc.date.issued2016-12-09-
dc.identifier.doi10.1080/03605302.2016.1269808-
dc.identifier.urihttp://hdl.handle.net/10754/603947-
dc.description.abstractWe study the emergence of gradient flows in Wasserstein distance as high friction limits of an abstract Euler flow generated by an energy functional. We develop a relative energy calculation that connects the Euler flow to the gradient flow in the diffusive limit regime. We apply this approach to prove convergence from the Euler-Poisson system with friction to the Keller-Segel system in the regime that the latter has smooth solutions. The same methodology is used to establish convergence from the Euler-Korteweg theory with monotone pressure laws to the Cahn-Hilliard equation.en
dc.description.sponsorshipAET was supported by funding from King Abdullah University of Science and Technology (KAUST).en
dc.language.isoenen
dc.publisherInforma UK Limiteden
dc.relation.urlhttp://arxiv.org/abs/1601.05966en
dc.rightsArchived with thanks to Communications in Partial Differential Equations.en
dc.titleFrom gas dynamics with large friction to gradient flows describing diffusion theoriesen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCommunications in Partial Differential Equationsen
dc.eprint.versionPost-printen
dc.contributor.institutionDipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Universita degli Studi dell’Aquila, Via Vetoio, I-67010 Coppito (L’Aquila) AQ, Italyen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
dc.identifier.arxivid1601.05966-

Version History

VersionItem Editor Date Summary
3 10754/603947grenzdm2016-12-13 07:24:59.085Accepted manuscript version received by email from Prof. Tzavaras.
1 10754/603947.1wangh0e2016-03-30 07:34:04.0
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