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

DOI

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.

Copyright

© 2008, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - R. Naz
AU  - Fazal M. Mahomed
AU  - David P. Mason
PY  - 2008
DA  - 2008/08/01
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  - 10.2991/jnmp.2008.15.s1.16
ID  - Naz2008
ER  -