We provide local formulae for the pressure of incompressible fuids. 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 Cα velocities have C 2α (or Lipschitz) pressures. We also give some regularity criteria for 3D incompressible Navier-Stokes equations.
All Science Journal Classification (ASJC) codes
- Euler's equations
- Navier-Stokes equations
- Regularity criteria