The Generalized Blasius equation revisited

The main subject of this paper is the model ( | f ″ | n − 1 f ″ ) ′ + 1 n + 1 f f ″ = 0 , f ( 0 ) = f ′ ( 0 ) = 0 , f ′ ( ∞ ) = 1 , arising in the study of a 2D laminar boundary-layer with power-law viscosity, f = f ( η ) is the non-dimensional stream function and n > 0 . Besides proving the existence and uniqueness results, we investigate the precise behavior of f for small and large η . In particular, for n > 1 we show that f ( η ) is linear for η ≥ η 0 > 0 . This means that in original ( x , y ) coordinates, the domain y ≥ a 0 x 1 n + 1 , a 0 = const . , the velocities u = const . , v = 0 and the boundary-layer is the domain y < a 0 x 1 n + 1 (“spatial localization of the layer”).