Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations
| hal.structure.identifier | Institut de Mathématiques de Jussieu [IMJ] | |
| dc.contributor.author | GALLAGHER, Isabelle | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAICU, Marius | |
| dc.date.accessioned | 2024-04-04T02:17:17Z | |
| dc.date.available | 2024-04-04T02:17:17Z | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 0002-9939 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189216 | |
| dc.description.abstractEn | In a 2001 paper, S. Montgomery-Smith provides a one-dimensional model for the three-dimensional, incompressible Navier-Stokes equations, for which he proves the blow-up of solutions associated with a class of large initial data, while the same global existence results as for the Navier-Stokes equations hold for small data. In this paper the model is adapted to the cases of two and three space dimensions, with the additional feature that the divergence-free condition is preserved. It is checked that a family of initial data constructed by Chemin and Gallagher, which is arbitrarily large yet generates a global solution to the Navier-Stokes equations in three space dimensions, actually causes blow-up for the toy model -- meaning that the precise structure of the nonlinear term is crucial to understanding the dynamics of large solutions to the Navier-Stokes equations. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations | |
| dc.type | Article de revue | |
| dc.subject.hal | Physique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph] | |
| dc.subject.hal | Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph] | |
| bordeaux.journal | Proceedings of the American Mathematical Society | |
| bordeaux.page | 2075-2083 | |
| bordeaux.volume | 137 | |
| 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-00994731 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00994731v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Proceedings%20of%20the%20American%20Mathematical%20Society&rft.date=2009&rft.volume=137&rft.issue=6&rft.spage=2075-2083&rft.epage=2075-2083&rft.eissn=0002-9939&rft.issn=0002-9939&rft.au=GALLAGHER,%20Isabelle&PAICU,%20Marius&rft.genre=article |
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