Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations

Kurzanzeige
dc.contributor.authorKlingenberg, Christian
dc.contributor.authorMarkfelder, Simon
dc.date.accessioned2024-12-11T12:10:32Z
dc.date.available2024-12-11T12:10:32Z
dc.date.issued2018-12
dc.description.abstractWe consider the 2-d isentropic compressible Euler equations. It was shown in [E. Chiodaroli, C. De Lellis and O. Kreml, Global ill-posedness of the isentropic system of gas dynamics, Comm. Pure Appl. Math. 68(7) (2015) 1157–1190] that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this paper, we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper, we will also show that there even exist Lipschitz initial data with the same property.
dc.description.versionpublisheddeu
dc.identifier.doi10.1142/s0219891618500224
dc.identifier.urihttps://kops.uni-konstanz.de/handle/123456789/71650
dc.language.isoeng
dc.subjectNon-uniqueness
dc.subjectCompressible Euler equations
dc.subject.ddc510
dc.titleNon-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equationseng
dc.typeJOURNAL_ARTICLE
dspace.entity.typePublication
kops.citation.bibtex
@article{Klingenberg2018-12Nonun-71650,
  year={2018},
  doi={10.1142/s0219891618500224},
  title={Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations},
  number={4},
  volume={15},
  issn={0219-8916},
  journal={Journal of Hyperbolic Differential Equations},
  pages={721--730},
  author={Klingenberg, Christian and Markfelder, Simon}
}
kops.citation.iso690KLINGENBERG, Christian, Simon MARKFELDER, 2018. Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations. In: Journal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), S. 721-730. ISSN 0219-8916. eISSN 1793-6993. Verfügbar unter: doi: 10.1142/s0219891618500224deu
kops.citation.iso690KLINGENBERG, Christian, Simon MARKFELDER, 2018. Non-uniqueness of energy-conservative solutions to the isentropic compressible two-dimensional Euler equations. In: Journal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), pp. 721-730. ISSN 0219-8916. eISSN 1793-6993. Available under: doi: 10.1142/s0219891618500224eng
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kops.sourcefieldJournal of Hyperbolic Differential Equations. World Scientific. 2018, <b>15</b>(4), S. 721-730. ISSN 0219-8916. eISSN 1793-6993. Verfügbar unter: doi: 10.1142/s0219891618500224deu
kops.sourcefield.plainJournal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), S. 721-730. ISSN 0219-8916. eISSN 1793-6993. Verfügbar unter: doi: 10.1142/s0219891618500224deu
kops.sourcefield.plainJournal of Hyperbolic Differential Equations. World Scientific. 2018, 15(4), pp. 721-730. ISSN 0219-8916. eISSN 1793-6993. Available under: doi: 10.1142/s0219891618500224eng
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source.periodicalTitleJournal of Hyperbolic Differential Equations
source.publisherWorld Scientific

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