Geodesic
On the result of He concerning the smoothness of solutions to the Navier-Stokes equations
Electronic journal of differential equations, Tome 2003 (2003)
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 
@article{EJDE_2003__2003__a190,
     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},
     year = {2003},
     volume = {2003},
     zbl = {1014.35073},
     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/