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
R. Naz, Fazal M. Mahomed, David P. Mason
Available Online 1 August 2008.
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- 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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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 -