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Local formulae for the hydrodynamic pressure and applications

2014; IOP Publishing; Volume: 69; Issue: 3 Linguagem: Inglês

10.1070/rm2014v069n03abeh004896

1473-2009

Peter Constantin,

Computational Fluid Dynamics and Aerodynamics

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 α velocities have C 2α (or Lipschitz) pressures.We also give some regularity criteria for 3D incompressible Navier-Stokes equations. Dedicated to the memory ofProfessor Mark I. Vishik.b(x, r) = p(x, r) + 1 4πr 2 ˆ|x-y|=r yx |y -x| • u(y) 2 dS(y).