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Weak solutions for Euler systems with non-local interactions

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dc.abstract.enWe consider several modifications of the Euler system of fluid dynamics, including its pressureless variant driven by non‐local interaction repulsive–attractive and alignment forces in the space dimension =2,3. These models arise in the study of self‐organization in collective behavior modeling of animals and crowds. We adapt the method of convex integration to show the existence of infinitely many global‐in‐time weak solutions for any bounded initial data. Then we consider the class of dissipative solutions satisfying, in addition, the associated global energy balance (inequality). We identify a large set of initial data for which the problem admits infinitely many dissipative weak solutions. Finally, we establish a weak–strong uniqueness principle for the pressure‐driven Euler system with non‐local interaction terms as well as for the pressureless system with Newtonian interaction.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorFeireisl, Eduard
dc.contributor.authorCarrillo, Jos\'e A.
dc.contributor.authorGwiazda, Piotr
dc.contributor.authorŚwierczewska-Gwiazda, Agnieszka
dc.date.accessioned2024-01-26T11:56:17Z
dc.date.available2024-01-26T11:56:17Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number3
dc.description.volume95
dc.identifier.doi10.1112/JLMS.12027
dc.identifier.issn0024-6107
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/124833
dc.identifier.weblinkhttps://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.12027
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofJournal of the London Mathematical Society
dc.relation.pages705-724
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.titleWeak solutions for Euler systems with non-local interactions
dc.typeJournalArticle
dspace.entity.typePublication