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Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data
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Robinson, James C. and Sadowski, Witold (2008) Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data. Asymptotic Analysis, Volume 59 (Number 1). pp. 39-50. doi:10.3233/ASY-2008-0899 ISSN 0921-7134.
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Official URL: http://dx.doi.org/10.3233/ASY-2008-0899
Abstract
Current theoretical results for the three-dimensional Navier-Stokes equations only guarantee that solutions remain regular for all time when the initial enstrophy (parallel to Du(0)parallel to(2) := integral vertical bar curl u(0 vertical bar)(2)) is sufficiently small, parallel to Du(0)parallel to(2) <= chi(0). In fact, this smallness condition is such that the enstrophy is always non-increasing. In this paper we provide a numerical procedure that will verify regularity of solutions for any bounded set of initial conditions, parallel to Du(0)parallel to(2) <= chi(1). Under the assumption that the equations are in fact regular we show that this procedure can be guaranteed to terminate after a finite time.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Navier-Stokes equations, Set theory | ||||
Journal or Publication Title: | Asymptotic Analysis | ||||
Publisher: | I O S Press | ||||
ISSN: | 0921-7134 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Volume 59 | ||||
Number: | Number 1 | ||||
Number of Pages: | 12 | ||||
Page Range: | pp. 39-50 | ||||
DOI: | 10.3233/ASY-2008-0899 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | Royal Society (Great Britain), Leverhulme Trust (LT), Poland, European Commission (EC) | ||||
Grant number: | 1 P03A 017 30 (GR-2331), SPADE2, MTKD-CT-2004-014508 |
Data sourced from Thomson Reuters' Web of Knowledge
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