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hal-00443881, version 9

## No blow-up of the 3D incompressible Euler equations

Léo Agélas () 1

(02/05/2011)

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 local geometry regularity of vortex lines leads to a strong dynamic depletion of the nonlinear vortex stretching, thus avoiding finite-time singularity formation. Then, we prove the existence and uniqueness of global strong solutions in $C([0,+\infty[;H^{r}(\mathbb{R}^3))^3$ with $r>\frac{7}{2}$, of the Euler equations as soon as the initial data $u_0\in H^{r}(\mathbb{R}^3)^3$. This result gives a positive answer to the open problem about existence and smoothness of solutions of Euler equations.

• 1 :  IFP Energies Nouvelles (IFPEN)
• IFP Energies Nouvelles

• hal-00443881, version 9
• oai:hal.archives-ouvertes.fr:hal-00443881
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• Soumis le : Mardi 3 Mai 2011, 00:03:01
• Dernière modification le : Mardi 3 Mai 2011, 11:56:01