Ohkitani, K. (2016) Study of the Navier–Stokes regularity problem with critical norms. Fluid Dynamics Research, 48 (2). 021401. ISSN 0169-5983
Abstract
We study the basic problems of regularity of the Navier–Stokes equations. The blowup criteria on the basis of the critical ${H}^{1/2}$-norm, is bounded from above by a logarithmic function, (Robinson et al 2012 J. Math. Phys. 53 115618). Assuming that the Cauchy–Schwarz inequality for the ${H}^{1/2}$-norm is not an overestimate, we replace it by a square-root of a product of the energy and the enstrophy. We carry out a simple asymptotic analysis to determine the time evolution of the energy. This generalises the (already ruled-out) self-similar blowup ansatz. Some numerical results are also presented, which support the above-mentioned replacement. We carry out a similar analysis for the four-dimensional Navier–Stokes equations.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 The Japan Society of Fluid Mechanics and IOP Publishing Ltd. This is an author produced version of a paper subsequently published in Fluid Dynamics Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Navier–Stokes equations; Leray equations; blowup; critical norms |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 24 Nov 2016 16:44 |
Last Modified: | 14 Apr 2017 02:59 |
Published Version: | https://doi.org/10.1088/0169-5983/48/2/021401 |
Status: | Published |
Publisher: | IOP Publishing |
Refereed: | Yes |
Identification Number: | 10.1088/0169-5983/48/2/021401 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:107858 |