Geodesic
Effect of hyperviscosity on the Navier-Stokes turbulence
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the conventional system as the regularization parameter approaches zero, for each dimension $d\leq 4$. Then we show that the use of this artificial viscosity term leads to truncated the number of degrees of freedom in the long-time behavior of the solutions to these equations. This result suggests that the hyperviscous Navier-Stokes system is an interesting model for three-dimensional fluid turbulence.
Classification : 76D05, 76F20, 35B30, 35B41, 35B65, 37L30, 37K40
Keywords: Navier-Stokes equations, hyperviscosity, weak solutions, attractor dimension, turbulence models 
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     author = {Younsi, Abdelhafid},
     title = {Effect of hyperviscosity on the {Navier-Stokes} turbulence},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a150/}
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Younsi, Abdelhafid. Effect of hyperviscosity on the Navier-Stokes turbulence. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a150/