Regularity of Navier--Stokes flows with bounds for the pressure
Date
05/2017Keywords
Metadata
Show full item recordAltmetrics Handle Statistics
Altmetrics DOI Statistics
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.
Citation
Tran , C V & Yu , X 2017 , ' Regularity of Navier--Stokes flows with bounds for the pressure ' , Applied Mathematics Letters , vol. 67 , pp. 21-27 . https://doi.org/10.1016/j.aml.2016.10.006
Publication
Applied Mathematics Letters
Status
Peer reviewed
ISSN
0893-9659Type
Journal article
Rights
© 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
Description
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 RES0020476Collections
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.