Electronic Journal of Differential Equations,
Vol. 2003(2003), No. 11, pp. 1-8.
Title: On the result of He concerning the smoothness of solutions to
the Navier-Stokes equations
Author: Milan Pokorny (Math. Institute of Charles Univ., Czech Republic)
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.