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Pressure moderation and effective pressure in Navier-Stokes flows

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Tran_2016_Pressure_Nonlinear_AAM.pdf (341.9Kb)
Date
17/08/2016
Author
Tran, Chuong Van
Yu, Xinwei
Keywords
Navier-Stokes equations
Pressure moderation
Effective pressure
Global regularity
QA Mathematics
QC Physics
T-NDAS
BDC
R2C
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Abstract
We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.
Citation
Tran , C V & Yu , X 2016 , ' Pressure moderation and effective pressure in Navier-Stokes flows ' , Nonlinearity , vol. 29 , no. 10 , pp. 2990-3005 . https://doi.org/10.1088/0951-7715/29/10/2990
Publication
Nonlinearity
Status
Peer reviewed
DOI
https://doi.org/10.1088/0951-7715/29/10/2990
ISSN
0951-7715
Type
Journal article
Rights
© 2016, IOP Publishing & London Mathematical Society. This work is 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 iopscience.iop.org / https://dx.doi.org/10.1088/0951-7715/29/10/2990
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/11499

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