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

Bibliographical note

Funding Information:
Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 and No. 2015R1A2A01002708 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ).

Publisher Copyright:
© 2017 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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