hal-00443881, version 10
No blow-up of Incompressible Euler equations in $\R^d$, $d\geq 2$
(17/05/2011)
Résumé : One of the most challenging questions in fluid dynamics is whether the incompressible Euler equations can develop a finite-time singularity from smooth initial data. In this paper, we found that small obstacle leads to strong dynamic depletion of the nonlinear vortex stretching, thus avoiding finite-time singularity formation. By passing to the limit in Euler equations in the exterior of an obstacle that shrinks to a point, we obtain Euler equation in the full space while keeping the depletion of the nonlinear term. Then, we prove the existence and uniqueness of global strong solutions in $C([0,+\infty[;W^{r,q}(\R^d))^d$ with $r>\frac{d}{q}+1$, $1
- 1 :
- IFP Energies Nouvelles
- Domaine : Mathématiques/Equations aux dérivées partielles
- Commentaire : 17 pages
- Versions disponibles : v1 (05-01-2010) v2 (31-01-2011) v3 (02-03-2011) v4 (04-03-2011) v5 (08-03-2011) v6 (28-03-2011) v7 (02-04-2011) v8 (26-04-2011) v9 (03-05-2011) v10 (17-05-2011) v11 (27-07-2011)
- hal-00443881, version 10
- http://hal.archives-ouvertes.fr/hal-00443881
- oai:hal.archives-ouvertes.fr:hal-00443881
- Contributeur :
- Soumis le : Mardi 17 Mai 2011, 01:24:55
- Dernière modification le : Mardi 17 Mai 2011, 08:34:25



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