REMARKS ON THE REGULARITY OF WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS

In this paper we extend the results of Foias-Guillope-Temam on the regularity and a priori estimates for the weak solutions of the Navier-Stokes equations. More specifically, we obtain upperbounds for the temporal averages of the Gevrey class norm for the weak solutions of the equations. The estimates are obtained first by getting integrated version of Foias-Temam's local in time estimate for Gevrey class norms of strong solutions and next by an induction procedure. We also strengthen slightly the local in time Gevrey class regularization of strong solutions.