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Nonclassical symmetry reductions of the three-dimensional incompressible Navier-Stokes equations
journal contribution
posted on 2023-05-18, 19:05 authored by Ludlow, DK, Clarkson, PA, Andrew BassomAndrew BassomThe 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.
History
Publication title
Journal of Physics A: Mathematical and GeneralVolume
31Issue
39Pagination
7965-7980ISSN
0305-4470Department/School
School of Natural SciencesPublisher
Iop Publishing LtdPlace of publication
Dirac House, Temple Back, Bristol, England, Bs1 6BeRepository Status
- Restricted