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

Research output: Contribution to journalArticle

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Author(s)

Chuong V. Tran, Xinwei Yu

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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.

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Details

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

    Research areas

  • Navier-Stokes equations, Hölder continuity , Global regularity

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ID: 246904105