Regularity criterion in terms of the oscillation of pressure for the 3D Navier-Stokes equations

We obtain a new regularity criterion in terms of the oscillation of time derivative of the pressure for the 3D Navier-Stokes equations in a domain D subset of R-3. The key observation for the proof is that the head pressure defined by (Q) over bar (x, t) = 1/2 vertical bar v(x, t)vertical bar(2) + (p) over bar (x, t), where (p) over bar (x, t) = p(x, t) - integral(t)(t0) sup(y is an element of Omega)(partial derivative(s)p(y, s) - vertical bar omega(y, s)vertical bar(2))ds with p(x, t) the pressure and omega the vorticity satisfies parabolic maximum principle in Omega x (t(0), T) with Omega (sic) D.