Local kinetic energy and singularities of the incompressible Navier–Stokes equations

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Abstract

We study the partial regularity problem of the incompressible Navier–Stokes equations. A reverse Hölder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to L(0,T;L3,w(R3)) where L3,w(R3) denotes the standard weak Lebesgue space.

Original languageEnglish
Pages (from-to)1171-1191
Number of pages21
JournalJournal of Differential Equations
Volume264
Issue number2
DOIs
Publication statusPublished - 2018 Jan 15

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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