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hal-00443881, version 10

## No blow-up of Incompressible Euler equations in $\R^d$, $d\geq 2$

Léo Agélas () 1

(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 (IFPEN)
• IFP Energies Nouvelles

• hal-00443881, version 10
• oai:hal.archives-ouvertes.fr:hal-00443881
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• Soumis le : Mardi 17 Mai 2011, 01:24:55
• Dernière modification le : Mardi 17 Mai 2011, 08:34:25