Local formulas for the hydrodynamic pressure and applications

Abstract

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.

References in corpus (1)

• Higher derivatives estimate for the 3D Navier-Stokes equation

Cited by in corpus (6)

• On the small-scale structure of turbulence and its impact on the pressure field
• Regularity results for rough solutions of the incompressible Euler equations via interpolation methods
• On Double Hölder Regularity of the Hydrodynamic Pressure in Bounded Domains
• Full double Hölder regularity of the pressure in bounded domains
• Hölder regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains
• Pressure, Intermittency, Singularity