Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations

Ludlow, David K. and Clarkson, Peter and Bassom, Andrew P. (1998) Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations. Journal of Physics A: Mathematical and General, 31 (39). pp. 7965-7980. ISSN 0305-4470. (The full text of this publication is not available from this repository)

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Official URL
http://dx.doi.org/10.1088/0305-4470/31/39/012

Abstract

The nonclassical reduction method as pioneered by Bluman and Cole (J.Meth. Mech. 18 1025-42) is used to examine symmetries of the full three-dimensional, unsteady, incompressible Navier-Stokes equations of fluid mechanics. The procedure, when applied to a system of partial differential equations, yields reduced sets of equations with one fewer independent variables. We find eight possibilities for reducing the Navier-Stokes equations in the three spatial and one temporal dimensions to sets of partial differential equations in three independent variables. Some of these reductions are derivable using the Lie-group method of classical symmetries but the remainder are genuinely nonclassical. Further investigations of one of our eight forms shows how it is possible to derive novel exact solutions of the Navier-Stokes equations by the nonclassical method.

Item Type: Article
Subjects: Q Science
Q Science > QC Physics > QC20 Mathematical Physics
Q Science > QC Physics
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science
Depositing User: M.A. Ziai
Date Deposited: 03 Apr 2009 00:41
Last Modified: 29 Apr 2014 14:26
Resource URI: http://kar.kent.ac.uk/id/eprint/17427 (The current URI for this page, for reference purposes)
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