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Steady solutions to viscous shallow water equations. The case of heavy water

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cris.lastimport.scopus2024-02-12T20:13:33Z
dc.abstract.enIn this note, we show the existence of regular solutions to the stationary version of the Navier–Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we are able to construct a solution, provided the total mass is sufficiently large. The main mathematical part is located in the construction of solutions. Uniqueness is impossible to obtain, since the gradient of the velocity is of magnitude of the force. The investigation is connected to the corresponding singular limit as Mach number goes to zero and methods for weak solutions to the compressible Navier–Stokes system.
dc.affiliationUniwersytet Warszawski
dc.contributor.authorAxmann, \v Simon
dc.contributor.authorMucha, Piotr
dc.contributor.authorPokorn\'y, Milan
dc.date.accessioned2024-01-26T08:10:13Z
dc.date.available2024-01-26T08:10:13Z
dc.date.issued2017
dc.description.financeNie dotyczy
dc.description.number5
dc.description.volume15
dc.identifier.doi10.4310/CMS.2017.V15.N5.A8
dc.identifier.issn1539-6746
dc.identifier.urihttps://repozytorium.uw.edu.pl//handle/item/120704
dc.identifier.weblinkhttps://doi.org/10.4310/CMS.2017.v15.n5.a8
dc.languageeng
dc.pbn.affiliationmathemathics
dc.relation.ispartofCommunications in Mathematical Sciences
dc.relation.pages1385-1402
dc.rightsClosedAccess
dc.sciencecloudnosend
dc.subject.ensteady compressible Navier–Stokes system
dc.subject.enshallow water equation
dc.subject.enlow Mach number limit
dc.subject.endensity-dependent viscosities
dc.subject.enlarge data
dc.subject.enexistence via Schauder type fixed point theorem
dc.titleSteady solutions to viscous shallow water equations. The case of heavy water
dc.typeJournalArticle
dspace.entity.typePublication