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Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations. (English) Zbl 1355.76017
Summary: In this article, we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional incompressible Navier-Stokes equations. Our results improve the classical $$L^{r}(0,T;L^{s})$$ regularity criteria for both velocity and pressure by factors of certain negative powers of the scaling invariant norms $$\|u\|_{L^3}$$ and $$\|u\|_{\dot{H}^{1 / 2}}$$.{
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