Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAICU, Marius | |
| hal.structure.identifier | Université Paris-Sud - Paris 11 [UP11] | |
| dc.contributor.author | REKALO, Andrey | |
| hal.structure.identifier | Laboratoire de Mathématiques d'Orsay [LMO] | |
| dc.contributor.author | RAUGEL, Geneviève | |
| dc.date.accessioned | 2024-04-04T02:17:24Z | |
| dc.date.available | 2024-04-04T02:17:24Z | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189225 | |
| dc.description.abstractEn | This paper is devoted to the large time behavior and especially to the regularity of the global attractor of the second grade fluid equations in the two-dimensional torus. We first recall that, for any size of the material coefficient alpha > 0, these equations are globally well posed and admit a compact global attractor A(alpha) in (H-3(T-2))(2). We prove that, for any alpha > 0, there exists beta(alpha) > 0, such that A(alpha) belongs to (H3+beta(alpha) (T-2))(2) if the forcing term is in (H1+beta(alpha) (T-2))(2). We also show that this attractor is contained in any Sobolev space (H3+m(T-2))(2) provided that alpha is small enough and the forcing term is regular enough. These arguments lead also to a new proof of the existence of the compact global attractor A(alpha). Furthermore we prove that on A(alpha), the second grade fluid system can be reduced to a finite-dimensional system of ordinary differential equations with an infinite delay. Moreover, the existence of a finite number of determining modes for the equations of the second grade fluid is established. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.title.en | Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.jde.2011.10.015 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| bordeaux.journal | Journal of Differential Equations | |
| bordeaux.page | 3695-3751 | |
| bordeaux.volume | 252 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 6 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00994720 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00994720v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20of%20Differential%20Equations&rft.date=2012&rft.volume=252&rft.issue=6&rft.spage=3695-3751&rft.epage=3695-3751&rft.eissn=0022-0396&rft.issn=0022-0396&rft.au=PAICU,%20Marius&REKALO,%20Andrey&RAUGEL,%20Genevi%C3%A8ve&rft.genre=article |
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