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

Chuong V. Tran; Xinwei Yu

doi:10.1016/j.aml.2016.10.006

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

Chuong V. Tran, Xinwei Yu

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	21-27
Number of pages	7
Journal	Applied Mathematics Letters
Volume	67
Early online date	1 Dec 2016
DOIs	https://doi.org/10.1016/j.aml.2016.10.006
Publication status	Published - May 2017

Keywords

Navier-Stokes equations
Hölder continuity
Global regularity

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10.1016/j.aml.2016.10.006

Tran_2016_Regularity_AML_AAM
© 2016, Elsevier. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.sciencedirect.com / https://dx.doi.org/10.1016/j.aml.2016.10.006
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Cite this

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title = "Regularity of Navier--Stokes flows with bounds for the pressure",

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.",

keywords = "Navier-Stokes equations, H{\"o}lder continuity , Global regularity",

author = "Tran, {Chuong V.} and Xinwei Yu",

note = "This paper was presented at the Warwick EPSRC Symposium on PDEs in Fluid Mechanics, September 2016. Part of this research was carried out when CVT was visiting the University of Alberta, whose hospitality is gratefully acknowledged. XY was partially supported by NSERC Discovery grant RES0020476",

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AU - Tran, Chuong V.

AU - Yu, Xinwei

N1 - This paper was presented at the Warwick EPSRC Symposium on PDEs in Fluid Mechanics, September 2016. Part of this research was carried out when CVT was visiting the University of Alberta, whose hospitality is gratefully acknowledged. XY was partially supported by NSERC Discovery grant RES0020476

PY - 2017/5

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N2 - 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.

AB - 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.

KW - Navier-Stokes equations

KW - Hölder continuity

KW - Global regularity

U2 - 10.1016/j.aml.2016.10.006

DO - 10.1016/j.aml.2016.10.006

M3 - Article

SN - 0893-9659

VL - 67

SP - 21

EP - 27

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

ER -

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

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Keywords

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