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A Refinement of the Local Serrin-Type Regularity Criterion for a Suitable Weak Solution to the Navier–Stokes Equations

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Abstract

We formulate a new criterion for regularity of a suitable weak solution v to the Navier–Stokes equations at the space-time point (x 0, t 0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of (x 0, t 0), intersected with the exterior of a certain space-time paraboloid with vertex at point (x 0, t 0). We make no special assumptions on the solution in the interior of the paraboloid.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Prague 1, Czech Republic

    Jiří Neustupa

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  1. Jiří Neustupa
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Correspondence to Jiří Neustupa.

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Communicated by V. Šverák

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Neustupa, J. A Refinement of the Local Serrin-Type Regularity Criterion for a Suitable Weak Solution to the Navier–Stokes Equations. Arch Rational Mech Anal 214, 525–544 (2014). https://doi.org/10.1007/s00205-014-0761-x

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  • DOI: https://doi.org/10.1007/s00205-014-0761-x

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