Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 12, pp. 1-9.

Title: Pressure conditions for the local regularity of solutions
       of the Navier-Stokes equations

Author: Mike O'Leary (Univ. of California, Santa Cruz, CA, USA.)

Abstract: 
We obtain a relationship between the integrability of the pressure
gradient and the the integrability of the velocity for local solutions
of the Navier--Stokes equations with finite energy. In particular, we show that
if the pressure gradient is sufficiently integrable, then the corresponding
velocity is locally bounded and smooth in the spatial variables. The result
is proven by using De Giorgi type estimates in $L^{\rm weak}_p$ spaces.

Submitted  January 26, 1998. Published May 13, 1998.
Math Subject Classification: 35Q30, 76D05. 
Key Words: Navier-Stokes; regularity; pressure.