Geodesic
Regularity of generalized Navier-Stokes equations in terms of direction of the velocity
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, the author studies the regularity of 3D generalized Navier-Stokes (GNS) equations with fractional dissipative terms $$ \frac{2 \alpha}{p} + \frac{3}{q} \leq 2 \alpha - \frac{3}{2},\quad \frac{6}{4 \alpha-3} q \leq \infty . $$ then any smooth on GNS in $[0,T)$ remains smooth on $[0, T]$.
Classification : 35D10, 35Q35, 76D03
Keywords: generalized Navier-Stokes equation, regularity, serrin criteria 
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     author = {Luo, Yuwen},
     title = {Regularity of generalized {Navier-Stokes} equations in terms of direction of the velocity},
     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__a172/}
}
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Luo, Yuwen. Regularity of generalized Navier-Stokes equations in terms of direction of the velocity. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a172/