Comptes Rendus
Probability Theory
An estimate for the vorticity of the Navier–Stokes equation
[Une estimation de la vorticité de l'équation de Navier–Stokes]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 89-92.

Supposons que u(,t) soit une solution de l'équation de Navier–Stokes sur le torus T3 de la dimension 3, et soit ω(,t)=×u(,t) la vorticité, nous démontrons dans cette Note que l'application

ω(,t)1+24νu(,t)22
est une fonction décroissante en t.

Let u(,t) be a strong solution of the Navier–Stokes equation on 3-dimensional torus T3, and ω(,t)=×u(,t) be the vorticity. In this Note we show that

ω(,t)1+24νu(,t)22
is decreasing in t as long as the solution u(,t) exists, where ν>0 is the viscosity constant and q denotes the Lq-norm.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.11.007

Zhongmin Qian 1

1 Mathematical Institute, University of Oxford, 24–29, St Giles', Oxford OX1 3LB, UK
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Zhongmin Qian. An estimate for the vorticity of the Navier–Stokes equation. Comptes Rendus. Mathématique, Volume 347 (2009) no. 1-2, pp. 89-92. doi : 10.1016/j.crma.2008.11.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.11.007/

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