Geodesic
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations
Electronic Journal of Differential Equations, Tome 2003 (2003).

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

Summary: We improve the regularity criterion for the Navier-Stokes equations proved by He [4]. We show that for the Cauchy problem the Leray-Hopf weak solution is smooth provided $\nabla u_3 \in L^t(0,T;L^s), \frac 2t + \frac 3s \leq \frac 32$.
Classification : 35Q35, 76D05
Keywords: Navier-Stokes equations, regularity of systems of PDE's, anisotropic regularity criteria 
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     author = {Pokorn\'y, Milan},
     title = {On the result of {He} concerning the smoothness of solutions to the {Navier-Stokes} equations},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a190/}
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Pokorný, Milan. On the result of He concerning the smoothness of solutions to the Navier-Stokes equations. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a190/