  We provide local formulas for the pressure of incompressible fluids. The
pressure can be expressed in terms of its average and averages of squares of
velocity increments in arbitrary small neighborhoods. As application, we give a
brief proof of the fact that $C^{\alpha}$ velocities have $C^{2\alpha}$ (or
Lipschitz) pressures. We also give some regularity criteria for 3D
incompressible Navier-Stokes equations.
