Solution of the model Lagerstrom problem (Q1905290)

We consider the problem \(v''(r) + {k \over r} v'(r) + v(r)v'(r) + \beta (v'(r))^2 = 0\), \(v(\varepsilon) = 0\), \(v(\infty) = 1\), where \(0 < \varepsilon \ll 1\), \(k \in \mathbb{N}\), and \(\beta \geq 0\) is a numerical parameter. This problem was proposed by Lagerstrom as the model problem for the Navier-Stokes equation with small Reynolds numbers. We show that not only an asymptotic solution but also the convergent solution of the above problem can be constructed by the fictitious parameter method.