Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data
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. ISSN 0921-7134Full text not available from this repository.
Official URL: http://dx.doi.org/10.3233/ASY-2008-0899
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|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Navier-Stokes equations, Set theory|
|Journal or Publication Title:||Asymptotic Analysis|
|Publisher:||I O S Press|
|Number of Pages:||12|
|Page Range:||pp. 39-50|
|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|
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