Show simple item record

dc.contributor.authorGiesselmann, Jan
dc.contributor.authorLattanzio, Corrado
dc.contributor.authorTzavaras, Athanasios
dc.date.accessioned2016-11-13T07:34:48Z
dc.date.available2015-12-02T12:44:51Z
dc.date.available2016-11-13T07:34:48Z
dc.date.issued2016-11-18
dc.identifier.issn1432-0673
dc.identifier.issn0003-9527
dc.identifier.doi10.1007/s00205-016-1063-2
dc.identifier.urihttp://hdl.handle.net/10754/583110
dc.description.abstractFor an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The latter, when applied to specific energies, yields relative energy identities for the Euler-Korteweg, the Euler-Poisson, the Quantum Hydrodynamics system, and low order approximations of the Euler-Korteweg system. For the Euler-Korteweg system we prove a stability theorem between a weak and a strong solution and an associated weak-strong uniqueness theorem. In the second part we focus on the Navier-Stokes-Korteweg system (NSK) with non-monotone pressure laws: we prove stability for the NSK system via a modified relative energy approach. We prove continuous dependence of solutions on initial data and convergence of solutions of a low order model to solutions of the NSK system. The last two results provide physically meaningful examples of how higher order regularization terms enable the use of the relative energy framework for models with energies which are not poly- or quasi-convex, but compensating via higher-order gradients.
dc.description.sponsorshipJG partially supported by the German Research Foundation (DFG) via SFB TRR 75 `Tropfendynamische Prozesse unter extremen Umgebungsbedingungen'. AET acknowledges the support of the King Abdullah University of Science and Technology (KAUST) and of the Aristeia program of the Greek Secretariat for Research through the project DIKICOMA.
dc.language.isoen
dc.publisherSpringer Nature
dc.relation.urlhttp://arxiv.org/abs/1510.00801
dc.rightsThe final publication is available at Springer via http://dx.doi.org/10.1007/s00205-016-1063-2
dc.titleRelative energy for the Korteweg theory and related Hamiltonian flows in gas dynamics
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalArchive for Rational Mechanics and Analysis
dc.eprint.versionPost-print
dc.contributor.institutionInstitute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 D-70563 Stuttgart Germany
dc.contributor.institutionDipartimento di Ingegneria e Scienze dell’Informazione e Matematica Universita degli Studi dell’Aquila Via Vetoio I-67010 Coppito (L’Aquila) AQ Italy
dc.contributor.institutionInstitute for Applied and Computational Mathematics Foundation for Research and Technology GR 70013 Heraklion, Crete Greece
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
dc.identifier.arxividarXiv:1510.00801
refterms.dateFOA2017-10-26T00:00:00Z
dc.date.published-online2016-11-18
dc.date.published-print2017-03
dc.date.posted2015-10-03


Files in this item

Thumbnail
Name:
hamflow.pdf
Size:
485.8Kb
Format:
PDF
Description:
Accepted Manuscript

This item appears in the following Collection(s)

Show simple item record

VersionItemEditorDateSummary

*Selected version