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A Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation

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dc.abstract.enA common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such cases most often related to the second law of thermodynamics. This observation easily generalizes to any symmetrizable system of conservation laws; they are endowed with nontrivial companion conservation laws, which are immediately satisfied by classical solutions. Not surprisingly, weak solutions may fail to satisfy companion laws, which are then often relaxed from equality to inequality and overtake the role of physical admissibility conditions for weak solutions. We want to answer the question: what is a critical regularity of weak solutions to a general system of conservation laws to satisfy an associated companion law as an equality? An archetypal example of such a result was derived for the incompressible Euler system in the context of Onsager’s conjecture in the early nineties. This general result can serve as a simple criterion to numerous systems of mathematical physics to prescribe the regularity of solutions needed for an appropriate companion law to be satisfied.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorGwiazda, Piotr
dc.contributor.authorŚwierczewska-Gwiazda, Agnieszka
dc.contributor.authorMichálek, Martin
dc.date.accessioned2024-01-24T18:04:31Z
dc.date.available2024-01-24T18:04:31Z
dc.date.copyright2018-03-23
dc.date.issued2018
dc.description.accesstimeAT_PUBLICATION
dc.description.financeNie dotyczy
dc.description.versionFINAL_PUBLISHED
dc.description.volume229
dc.identifier.doi10.1007/S00205-018-1238-0
dc.identifier.issn0003-9527
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/101756
dc.identifier.weblinkhttps://link.springer.com/article/10.1007%2Fs00205-018-1238-0
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofArchive for Rational Mechanics and Analysis
dc.relation.pages1223–1238
dc.rightsCC-BY
dc.sciencecloudnosend
dc.titleA Note on Weak Solutions of Conservation Laws and Energy/Entropy Conservation
dc.typeJournalArticle
dspace.entity.typePublication