On regularity of stationary stokes and navier-stokes equations near boundary

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We obtain local estimates of the steady-state Stokes system "without pressure" near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations in a smooth domain in five dimension.

Original languageEnglish
Pages (from-to)78-101
Number of pages24
JournalJournal of Mathematical Fluid Mechanics
Issue number1
Publication statusPublished - 2004

Bibliographical note

Funding Information:
Acknowledgement. This research was supported in part by NSF Grant No. DMS-9877055. The author expresses his deep gratitude to his advisor, Professor Vladimír Sˇverák for guidance and encouragement. The author also thanks referees for helpful comments.

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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