Remarks on the Smoothness of the $L^{\infty}(0,T;L^{3})$ Solutions of the 3-D Navier-Stokes Equations

H. Beir\ ao da Veiga

Abstract: In this note we consider the $L^{\infty}(0,T;L^{3}(\Omega))$ solutions of the Navier-Stokes equations, where $\Omega$ is a domain of $\R^{3}$. We give a very simple proof of a sufficient condition for regularity of solutions. This condition contains, as a quite particular case, continuity from the left on $(0,T]$ with values in $L^{3}(\Omega)$. See Theorem 2.2 below.

Keywords: Navier-Stokes equations; regularity.

Classification (MSC2000): 35B65, 35K55, 76D05

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