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Two component regularity for the Navier-Stokes equationsKeywords: Navier-Stokes equations , regularity criterion , two component , multiplier spaces , Besov spaces Abstract: 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 $ ablawidetilde{u}$ satisfy Serrin's type criterion.
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