Existence of energy-variational solutions to hyperbolic conservation laws
| dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
| dc.bibliographicCitation.volume | 2974 | |
| dc.contributor.author | Eiter, Thomas | |
| dc.contributor.author | Lasarzik, Robert | |
| dc.date.accessioned | 2026-03-23T14:08:38Z | |
| dc.date.available | 2026-03-23T14:08:38Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We introduce the concept of energy-variational solutions for hyperbolic conservation laws. Intrinsically, these energy-variational solutions fulfill the weak-strong uniqueness principle and the semi-flow property, and the set of solutions is convex and weakly-star closed. The existence of energy-variational solutions is proven via a suitable time-discretization scheme under certain assumptions. This general result yields existence of energy-variational solutions to the magnetohydrodynamical equations for ideal incompressible fluids and to the Euler equations in both the incompressible and the compressible case. Moreover, we show that energy-variational solutions to the Euler equations coincide with dissipative weak solutions. | eng |
| dc.description.version | publishedVersion | eng |
| dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/33315 | |
| dc.identifier.uri | https://doi.org/10.34657/32383 | |
| dc.language.iso | eng | |
| dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
| dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2974 | |
| dc.relation.essn | 2198-5855 | |
| dc.relation.hasversion | https://doi.org/10.1007/s00526-024-02713-9 | |
| dc.relation.issn | 0946-8633 | |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
| dc.subject.ddc | 510 | eng |
| dc.subject.other | Existence | eng |
| dc.subject.other | generalized solutions | eng |
| dc.subject.other | conservation laws | eng |
| dc.subject.other | time discretization | eng |
| dc.subject.other | weak-strong | eng |
| dc.subject.other | uniqueness | eng |
| dc.subject.other | Euler equations | eng |
| dc.title | Existence of energy-variational solutions to hyperbolic conservation laws | eng |
| dc.type | Report | eng |
| tib.accessRights | openAccess | |
| wgl.contributor | WIAS | |
| wgl.subject | Mathematik | |
| wgl.type | Report / Forschungsbericht / Arbeitspapier |
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