Solution
= Solution
The only vorticity component is $ω=(1/r)(rv)\prime$. Its steady equation is $-αrω\prime=2αω+ν(ω\prime\prime+r^{-1}ω\prime)$, solved by $ω=ω_0e^{-αr^2/(2ν)}$. Regularity at zero gives
$$
v(r)={ω_0ν\over αr}(1-e^{-αr^2/(2ν)}).
$$
Its maximum satisfies $e^s=1+2s$, $s=αr^{*2}/(2ν)$, so $r^*=O(\sqrt{ν/α})$.