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Archive for Rational Mechanics and Analysis

, Volume 228, Issue 1, pp 237–277 | Cite as

The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier–Stokes Equations

  • Diego ChamorroEmail author
  • Pierre-Gilles Lemarié-Rieusset
  • Kawther Mayoufi
Article

Abstract

We study the role of the pressure in the partial regularity theory for weak solutions of the Navier–Stokes equations. By introducing the notion of dissipative solutions, due to Duchon and Robert (Nonlinearity 13:249–255, 2000), we will provide a generalization of the Caffarelli, Kohn and Nirenberg theory. Our approach sheels new light on the role of the pressure in this theory in connection to Serrin’s local regularity criterion.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Diego Chamorro
    • 1
    Email author
  • Pierre-Gilles Lemarié-Rieusset
    • 1
  • Kawther Mayoufi
    • 1
  1. 1.Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), UMR CNRS 8071 and ENSIIE, Université d’Evry Val d’Essonne, IBGBIEvry CedexFrance

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