In this paper we consider the Cauchy problem for the $n$ -dimensional Navier-Stokes equations and we prove a regularity criterion for weak solutions involving the summability of the pressure. Related results for the initial-boundary value problem are also presented.

In this paper we study the finite element approximation of systems of p-Stokes type for $p \in (1,\infty)$. We derive (in some cases optimal) error estimates for finite element approximation of the velocity and for the pressure in a suitable functional setting. The results are supported by numerical experiments.