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 1 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 (Online)
1776-0852
ISSN (Print)
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  - 1776-0852
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  -