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

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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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Authors and Affiliations

  1. Laboratoire de Mathématiques et Modélisation d’Evry (LaMME), UMR CNRS 8071 and ENSIIE, Université d’Evry Val d’Essonne, IBGBI, 23 Boulevard de France, 91037, Evry Cedex, France

    Diego Chamorro, Pierre-Gilles Lemarié-Rieusset & Kawther Mayoufi

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  1. Diego Chamorro
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  2. Pierre-Gilles Lemarié-Rieusset
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  3. Kawther Mayoufi
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Correspondence to Diego Chamorro.

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Communicated by P. Constantin

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Chamorro, D., Lemarié-Rieusset, PG. & Mayoufi, K. The Role of the Pressure in the Partial Regularity Theory for Weak Solutions of the Navier–Stokes Equations. Arch Rational Mech Anal 228, 237–277 (2018). https://doi.org/10.1007/s00205-017-1191-3

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  • DOI: https://doi.org/10.1007/s00205-017-1191-3

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