Electron. J. Diff. Eqns., Vol. 2003(2003), No. 11, pp. 1-8.

On the result of He concerning the smoothness of solutions to the Navier-Stokes equations

Milan Pokorny

Abstract:
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 $\nabla u_3 \in L^t(0,T;L^s)$, $\frac 2t + \frac 3s \leq \frac 32$.

Submitted November 6, 2002. Published February 6, 2003.
Math Subject Classifications: 35Q35, 76D05.
Key Words: Navier-Stokes equations, regularity of systems of PDE's, anisotropic regularity criteria.

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Milan Pokorny
Math. Institute of Charles University
Sokolovska 83, 186 75 Praha 8, Czech Republic
e-mail: pokorny@karlin.mff.cuni.cz

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