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The Oseen and Navier-Stokes equations in a non-solenoidal framework

 

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dc.creator Amrouche, Chérif es
dc.creator Rodríguez Bellido, María Ángeles es
dc.date.accessioned 2016-07-05T10:03:05Z
dc.date.available 2016-07-05T10:03:05Z
dc.date.issued 2014-12-11
dc.identifier.citation Amrouche, C. y Rodríguez Bellido, M.Á. (2014). The Oseen and Navier-Stokes equations in a non-solenoidal framework. Mathematical Methods in the Applied Sciences, 39 (17), 5066-5090.
dc.identifier.issn 0170-4214 es
dc.identifier.issn 1099-1476 es
dc.identifier.uri http://hdl.handle.net/11441/43149
dc.description.abstract The very weak solution for the Stokes, Oseen and Navier-Stokes equations has been studied by several authors in the last decades in domains of Rn, n ≥ 2. The authors studied the Oseen and Navier-Stokes problems assuming a solenoidal convective velocity in a bounded domain Ω ⊂ R3 of class C1,1 for v ∈ Ls (Ω) for s ≥ 3 in some previous papers. The results for the Navier-Stokes equations were obtained by using a fixed-point argument over the Oseen problem. These results improve those of Galdi et al. , Farwig et al. and Kim for the Navier-Stokes equations, because a less regular domain Ω ⊂ R3 and more general hypothesis on the data are considered. In particular, the external forces must not be small. In this work, existence of weak, strong, regularised and very weak solution for the Oseen problem are proved, mainly assuming that v ∈ L3(Ω) and its divergence ∇ · v is sufficiently small in the W−1,3(Ω)-norm. In this sense, one extends the analysis made by the authors for a given solenoidal v in some previous papers. As a consequence, the existence of very weak solution for the Navier-Stokes problem (u, π) ∈ L3(Ω) × W−1,3(Ω)/R for a non-zero divergence condition is obtained in the 3D case. es
dc.description.sponsorship Ministerio de Ciencia e Innovación (España) MTM2009-12927 es
dc.description.sponsorship Ministerio de Economía y Competitividad MTM2012-32325 es
dc.format application/pdf es
dc.language.iso eng es
dc.publisher Wiley es
dc.relation.ispartof Mathematical Methods in the Applied Sciences, 39 (17), 5066-5090.
dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional *
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ *
dc.subject Oseen equations es
dc.subject Navier-Stokes equations es
dc.subject Very weak solutions es
dc.subject Stationary solutions es
dc.title The Oseen and Navier-Stokes equations in a non-solenoidal framework es
dc.type info:eu-repo/semantics/article es
dc.type.version info:eu-repo/semantics/acceptedVersion es
dc.rights.accessrights info:eu-repo/semantics/openAccess es
dc.contributor.affiliation Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico es
dc.relation.projectID MTM2009-12927 es
dc.relation.projectID info:eu-repo/grantAgreement/MINECO/MTM2012-32325 es
dc.relation.publisherversion http://dx.doi.org/10.1002/mma.3337 es
dc.identifier.doi 10.1002/mma.3337 es
dc.contributor.group Universidad de Sevilla. FQM131: Ec.diferenciales,Simulacion Num.y Desarrollo Software es
idus.format.extent 42 p. es
dc.journaltitle Mathematical Methods in the Applied Sciences es
dc.publication.volumen 39 es
dc.publication.issue 17 es
dc.publication.initialPage 5066 es
dc.publication.endPage 5090 es
dc.identifier.idus https://idus.us.es/xmlui/handle/11441/43149
dc.contributor.funder Ministerio de Ciencia e Innovación (MICIN). España
dc.contributor.funder Ministerio de Economía y Competitividad (MINECO). España
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