Regularity of Navier--Stokes flows with bounds for the pressure

Chuong V. Tran, Xinwei Yu

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
3 Downloads (Pure)

Abstract

This study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.

Original languageEnglish
Pages (from-to)21-27
Number of pages7
JournalApplied Mathematics Letters
Volume67
Early online date1 Dec 2016
DOIs
Publication statusPublished - May 2017

Keywords

  • Navier-Stokes equations
  • Hölder continuity
  • Global regularity

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