Sufficient conditions for the regularity of the solutions of the Navier-Stokes equations

In this paper we find sufficient conditions, involving only the pressure, that ensure the regularity of weak solutions to the Navier-Stokes equations. Conditions involving only the pressure were previously obtained in [7, 4]. Following a remark in this last reference we improve, in particular, Kaniel's result [7]. Our condition can be seen at the light of the heuristic idea that the pressure behaves similarly to the modulus squared of the velocity. Copyright (C) 1999 John Wiley & Sons, Ltd.