= Solution
For $n>1$, the exponent $m=2/(n+1)$ in $U'=-A|U-U_\infty|^m$ 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.
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