Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 352 / 1 / b / v

For $n>1$, the exponent $m=2/(n+1)$ in $U^{\prime }=-A|U-U_{\infty }{|}^m$ is below one. Its integral reaches $U=U_{\infty }$ at a finite distance, after which the constant far-field solution can be attached. The ideal power law therefore predicts a compactly supported transition with finite-width edges rather than the algebraic tails found for $n<1$. Near those edges horizontal shear vanishes and the neglected vertical or regularizing physics becomes important, so the sharp termination should not be interpreted literally.