Local formulae for the hydrodynamic pressure and applications

Abstract

We provide local formulae for the pressure of incompressible fluids. The pressure can be expressed in terms of its average and averages of squares of velocity increments in arbitrarily small neighbourhoods. As an application, we give a brief proof of the fact that C α velocities have C 2 α (or Lipschitz) pressures. We also give some regularity criteria for 3D incompressible Navier–Stokes equations.