Geodesic
Local formulae for the hydrodynamic pressure and applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 395-418

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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 $C^{\alpha}$ velocities have $C^{2\alpha}$ (or Lipschitz) pressures. We also give some regularity criteria for 3D incompressible Navier–Stokes equations. Bibliography: 9 titles.
Keywords: Navier–Stokes equations, pressure, regularity criteria.
Mots-clés : Euler's equations 
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     author = {P. Constantin},
     title = {Local formulae for the hydrodynamic pressure and applications},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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     volume = {69},
     number = {3},
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     url = {http://geodesic.mathdoc.fr/item/RM_2014_69_3_a0/}
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P. Constantin. Local formulae for the hydrodynamic pressure and applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 69 (2014) no. 3, pp. 395-418. http://geodesic.mathdoc.fr/item/RM_2014_69_3_a0/