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The classical Kelvin-Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity
| dc.contributor.author | Antontsev, S. N. | |
| dc.contributor.author | Oliveira, H. B. de | |
| dc.contributor.author | Khompysh, Kh | |
| dc.date.accessioned | 2021-09-08T10:57:56Z | |
| dc.date.available | 2021-09-08T10:57:56Z | |
| dc.date.issued | 2021-05 | |
| dc.description.abstract | The classical Kelvin-Voigt equations for incompressible fluids with non-constant density are investigated in this work. To the associated initial-value problem endowed with zero Dirichlet conditions on the assumed Lipschitz-continuous boundary, we prove the existence of weak solutions: velocity and density. We also prove the existence of a unique pressure. These results are valid for d is an element of {2, 3, 4}. In particular, if d is an element of {2, 3}, the regularity of the velocity and density is improved so that their uniqueness can be shown. In particular, the dependence of the regularity of the solutions on the smoothness of the given data of the problem is established. | |
| dc.description.sponsorship | RSF, Russian Federation [19-11-00069]; Portuguese Foundation for Science and Technology, PortugalPortuguese Foundation for Science and Technology [UID/MAT/04561/2019]; Ministry of Education and Science of the Republic of Kazakhstan (MES RK), Kazakhstan [AP08052425] | |
| dc.identifier.doi | 10.1088/1361-6544/abe51e | |
| dc.identifier.issn | 0951-7715 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/16979 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | IOP PUBLISHING LTD | |
| dc.subject | Kelvin– | |
| dc.subject | Voigt equations | |
| dc.subject | Existence | |
| dc.subject | Regularity | |
| dc.subject | Uniqueness | |
| dc.subject | Incompressible fluids with non-constant density | |
| dc.subject.other | Mathematics; Physics | |
| dc.title | The classical Kelvin-Voigt problem for incompressible fluids with unknown non-constant density: existence, uniqueness and regularity | |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/154734/PT | |
| oaire.citation.endPage | 3111 | |
| oaire.citation.issue | 5 | |
| oaire.citation.startPage | 3083 | |
| oaire.citation.title | Nonlinearity | |
| oaire.citation.volume | 34 | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| person.familyName | Borges de Oliveira | |
| person.givenName | Hermenegildo | |
| person.identifier.ciencia-id | 4A15-7156-6A00 | |
| person.identifier.orcid | 0000-0001-9053-8442 | |
| person.identifier.rid | F-3186-2014 | |
| person.identifier.scopus-author-id | 7004475473 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | |
| rcaap.type | article | |
| relation.isAuthorOfPublication | 6f0df0e9-24bf-43d5-97b3-4a709a59e2b5 | |
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