The Generalized Blasius equation revisited

The main subject of this paper is the model (|f″|n−1f″)′+1n+1ff″=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)f=f(η) is the non-dimensional stream function and n>0n>0. Besides proving the existence and uniqueness results, we investigate the precise behavior of ff for small and large ηη. In particular, for n>1n>1 we show that f(η)f(η) is linear for η≥η0>0η≥η0>0. This means that in original (x,y)(x,y) coordinates, the domain y≥a0x1n+1,a0=const., the velocities u=const.,v=0 and the boundary-layer is the domain y