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Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations

Ludlow, David K., Clarkson, Peter, Bassom, Andrew P. (1999) Similarity reductions and exact solutions for the two-dimensional incompressible Navier-Stokes equations. Studies in Applied Mathematics, 103 (3). pp. 183-240. ISSN 0022-2526. (doi:10.1111/1467-9590.00125) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:16911)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL:
http://dx.doi.org/10.1111/1467-9590.00125

Abstract

We study similarity reductions and exact solutions of the (2+1)-dimensional incompressible Navier-Stokes equations using the direct method originally developed by Clarkson and Kruskal [37]. The Navier-Stokes equations are reduced to their conventional stream function form, and it is shown that there exist essentially five reductions into lower-order partial differential equations. Furthermore, we study the possibilities for reducing each of these five forms to ordinary differential equations, some of which can be solved analytically, while others necessitate numerical treatment, In particular we exhibit several new reductions that are not obtained using the classical Lie group method of infinitesimal transformations, and thus we generate new exact solutions of the governing equations. Some of our solutions admit physical interpretations, and many of them contain well-known Navier-Stokes solutions as special examples.

Item Type: Article
DOI/Identification number: 10.1111/1467-9590.00125
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: I.T. Ekpo
Date Deposited: 08 Apr 2009 09:37 UTC
Last Modified: 16 Nov 2021 09:54 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/16911 (The current URI for this page, for reference purposes)

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