Journal of Nonlinear Mathematical Physics

Volume 15, Issue Supplement 1, August 2008, Pages 179 - 191

Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations

Authors
R. Naz, Fazal M. Mahomed, David P. Mason
Corresponding Author
R. Naz
Available Online 25 August 2008.
DOI
https://doi.org/10.2991/jnmp.2008.15.s1.16How to use a DOI?
Abstract
The similarity solution to Prandtl’s boundary layer equations for two-dimensional and radial flows with vanishing or constant mainstream velocity gives rise to a third-order ordinary differential equation which depends on a parameter ?. For special values of ? the third-order ordinary differential equation admits a three-dimensional symmetry Lie algebra L3. For solvable L3 the equation is integrated by quadrature. For non-solvable L3 the equation reduces to the Chazy equation. The Chazy equation is reduced to a first-order differential equation in terms of differential invariants which is transformed to a Riccati equation. In general the third-order ordinary differential equation admits a two-dimensional symmetry Lie algebra L2. For L2 the differential equation can only be reduced to a first-order equation. The invariant solutions of the third-order ordinary differential equation are also derived.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
15 - 100
Pages
179 - 191
Publication Date
2008/08
ISSN
1402-9251
DOI
https://doi.org/10.2991/jnmp.2008.15.s1.16How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - R. Naz
AU  - Fazal M. Mahomed
AU  - David P. Mason
PY  - 2008
DA  - 2008/08
TI  - Symmetry Solutions of a Third-Order Ordinary Differential Equation which Arises from Prandtl Boundary Layer Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 179
EP  - 191
VL  - 15
IS  - Supplement 1
SN  - 1402-9251
UR  - https://doi.org/10.2991/jnmp.2008.15.s1.16
DO  - https://doi.org/10.2991/jnmp.2008.15.s1.16
ID  - Naz2008
ER  -