Imperial College London
Professor John Gibbon

ProfessorJohnGibbon

Faculty of Natural Sciences, Department of Mathematics

Senior Research Investigator
 
 
 
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Contact

 

j.d.gibbon Website

 
 
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Location

 

6M41Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Gibbon:2014:10/2605,
author = {Gibbon, JD and Donzis, DA and Gupta, A and Kerr, RM and Pandit, R and Vincenzi, D},
doi = {10/2605},
journal = {Nonlinearity},
pages = {2605--2625},
title = {Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations},
url = {http://dx.doi.org/10.1088/0951-7715/27/10/2605},
volume = {27},
year = {2014}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The periodic 3D Navier–Stokes equations are analyzed in terms of dimensionless, scaled, L2m-norms of vorticity Dm (1 ≤ m < ∞). The first in this hierarchy, D1, is the global enstrophy. Three regimes naturally occur in the D1 − Dm plane. Solutions in the first regime, which lie between two concave curves, are shown to be regular, owing to strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics lie in this heavily depleted regime [1]; new numerical evidence for this is presented. Estimates for the dimension of a global attractor and a corresponding inertial range are given for this regime. However, two more regimes can theoretically exist. In the second, which lies between the upper concave curve and a line, the depletion is insufficient to regularize solutions, so no more than Leray's weak solutions exist. In the third, which lies above this line, solutions are regular, but correspond to extreme initial conditions. The paper ends with a discussion on the possibility of transition between these regimes.
AU  - Gibbon,JD
AU  - Donzis,DA
AU  - Gupta,A
AU  - Kerr,RM
AU  - Pandit,R
AU  - Vincenzi,D
DO  - 10/2605
EP  - 2625
PY  - 2014///
SN  - 0951-7715
SP  - 2605
TI  - Regimes of nonlinear depletion and regularity in the 3D Navier-Stokes equations
T2  - Nonlinearity
UR  - http://dx.doi.org/10.1088/0951-7715/27/10/2605
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000342751000007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
VL  - 27
ER  -
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