Abstract
In this paper, we establish a Serrin-type regularity criterion in terms of the pressure for Leray weak solutions to the Navier-Stokes equation in R-3. It is proved that the solution is regular if the associate pressure satifies
p is an element of L2/2-r ((0,T); <(M)over dot>(2,3/r) (R-3)) or del p is an element of L2/3-r ((0,T); <(M)over dot>(2,3/r) (R-3))
for 0 < r < 1, where <(M)over dot>(2,3/r) (R-3) is the critical Morrey-Campanto space. Regularity criteria for the 3D MHD equations are also given.