Geodesic
Two component regularity for the Navier-Stokes equations
Electronic journal of differential equations, Tome 2009 (2009)
We consider the regularity of weak solutions to the Navier-Stokes equations in $\mathbb{R}^3$. Let $u:=(u_1,u_2,u_3)$ be a weak solution and $\widetilde{u}:=(u_1,u_2,0)$. We prove that $u$ is strong solution if $\nabla\widetilde{u}$ satisfy Serrin's type criterion.
Classification : 35Q30, 35K15, 76D03
Keywords: Navier-Stokes equations, regularity criterion, two component, multiplier spaces, Besov spaces 
@article{EJDE_2009__2009__a19,
     author = {Fan,  Jishan and Gao,  Hongjun},
     title = {Two component regularity for the {Navier-Stokes} equations},
     journal = {Electronic journal of differential equations},
     year = {2009},
     volume = {2009},
     zbl = {1178.35287},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a19/}
}
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Fan,  Jishan; Gao,  Hongjun. Two component regularity for the Navier-Stokes equations. Electronic journal of differential equations, Tome 2009 (2009). http://geodesic.mathdoc.fr/item/EJDE_2009__2009__a19/