Stability properties of the Euler-Korteweg system with nonmonotone pressures

Handle URI:
http://hdl.handle.net/10754/621819
Title:
Stability properties of the Euler-Korteweg system with nonmonotone pressures
Authors:
Giesselmann, Jan; Tzavaras, Athanasios ( 0000-0002-1896-2270 )
Abstract:
We establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.
KAUST Department:
Computer, Electrical, Mathematical Sciences & Engineering Division
Publisher:
Informa UK Limited
Journal:
Applicable Analysis
Issue Date:
21-Dec-2016
DOI:
10.1080/00036811.2016.1276175
ARXIV:
1611.01663
Type:
Article
ISSN:
1563-504X; 0003-6811
Sponsors:
JG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.
Additional Links:
https://arxiv.org/abs/1611.01663
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorGiesselmann, Janen
dc.contributor.authorTzavaras, Athanasiosen
dc.date.accessioned2016-12-22T06:35:05Z-
dc.date.available2016-11-13T08:18:34Z-
dc.date.available2016-12-22T06:35:05Z-
dc.date.issued2016-12-21-
dc.identifier.issn1563-504Xen
dc.identifier.issn0003-6811en
dc.identifier.doi10.1080/00036811.2016.1276175-
dc.identifier.urihttp://hdl.handle.net/10754/621819-
dc.description.abstractWe establish a relative energy framework for the Euler-Korteweg system with non-convex energy. This allows us to prove weak-strong uniqueness and to show convergence to a Cahn-Hilliard system in the large friction limit. We also use relative energy to show that solutions of Euler-Korteweg with convex energy converge to solutions of the Euler system in the vanishing capillarity limit, as long as the latter admits sufficiently regular strong solutions.en
dc.description.sponsorshipJG thanks the Baden-Wurttemberg foundation for support via the project ’Numerical Methods for Multiphase Flows with Strongly Varying Mach Numbers’.en
dc.language.isoenen
dc.publisherInforma UK Limiteden
dc.relation.urlhttps://arxiv.org/abs/1611.01663en
dc.rightsThis is the accepted manuscript version of an article published in Applicable Analysis. The final, publisher version can be found at: http://dx.doi.org/10.1080/00036811.2016.1276175en
dc.titleStability properties of the Euler-Korteweg system with nonmonotone pressuresen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical, Mathematical Sciences & Engineering Divisionen
dc.identifier.journalApplicable Analysisen
dc.eprint.versionPost-printen
dc.contributor.institutionInstitute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, D-70563 Stuttgart, Germanyen
dc.identifier.arxivid1611.01663-
kaust.authorTzavaras, Athanasiosen

Version History

VersionItem Editor Date Summary
2 10754/621819grenzdm2016-12-22 06:27:48.766Accepted manuscript and DOI received from Prof. Tzavaras.
1 10754/621819.1grenzdm2016-11-13 08:18:34.0
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