Ludlow, David K.,
Clarkson, Peter,
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.
(doi:10.1088/0305-4470/31/39/012)
(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:17427)

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/10.1088/0305-4470/31/39/012 |

## 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 |
---|---|

DOI/Identification number: | 10.1088/0305-4470/31/39/012 |

Subjects: |
Q Science Q Science > QC Physics > QC20 Mathematical Physics Q Science > QC Physics |

Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |

Depositing User: | M.A. Ziai |

Date Deposited: | 03 Apr 2009 00:41 UTC |

Last Modified: | 16 Nov 2021 09:55 UTC |

Resource URI: | https://kar.kent.ac.uk/id/eprint/17427 (The current URI for this page, for reference purposes) |

Clarkson, Peter: | https://orcid.org/0000-0002-8777-5284 |

- Export to:
- RefWorks
- EPrints3 XML
- BibTeX
- CSV

- Depositors only (login required):