Repositorio de producción científica de la Universidad de Sevilla

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

 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 es divergence condition is obtained in the 3D case. 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
Size: 754.9Kb
Format: PDF