The Minkowski dimension of boundary singular points in the Navier–Stokes equations

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Abstract

We study the partial regularity problem of the three-dimensional incompressible Navier–Stokes equations. We present a new boundary regularity criterion for boundary suitable weak solutions. As an application, a bound for the parabolic Minkowski dimension of possible singular points on the boundary is obtained.

Original languageEnglish
Pages (from-to)4705-4718
Number of pages14
JournalJournal of Differential Equations
Volume267
Issue number8
DOIs
Publication statusPublished - 2019 Oct 5

Bibliographical note

Funding Information:
We would like to thank to the referee for his careful reading of the work and has helpful suggestions. We would also like to thank to Dr. Yanqing Wang for his comments on the first draft. Hi Jun Choe has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2015R1A5A1009350 ). Minsuk Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1C1B2015731 ) and (No. 2015R1A5A1009350 ) and by the Yonsei University Research Fund of 2018-22-0046 .

Publisher Copyright:
© 2019 Elsevier Inc.

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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