Symmetries and heir equations for the laminar boundary layer model
The nonclassical symmetry method for finding exact solutions of partial differential equations consists in postulating a new requirement (the invariant surface condition) compatible with the primary system of equations. This compatibility condition with uncertain coefficients yields another (heir) system, and the procedure can be repeated. Using this method, the authors precisely analyze explicit solutions of the Prandtl system \[ uu_x+ vu_y=w_y,\quad u_x+v_y=0,\quad u_y=w \] governing an incompressible viscous fluid moving near a thin plate with steady flow and zero pressure gradient. Calculations are stated with details up to third iteration, and interrelations to the classical Lie algebra invariance are discussed.
scientific article; zbMATH DE number 930230