New results of Falkner-Skan equation arising in boundary layer theory
The Falkner-Skan equation is a parameter dependent, third order non-linear ordinary differential equation arising in the theory of two-dimensional incompressible boundary layer theory. It is known that when the parameter \(\lambda\) is non-negative the Falkner-Skan equation is well-posed. On the other hand, there exists a negative real number \(\lambda^*\) such that there are no solutions for \(\lambda < \lambda^*\), exactly one for \(\lambda = \lambda^*\), and at least one for \(\lambda \in (\lambda^*, 0)\). In the paper under review, the author uses an equivalent singular integral equation to establish new properties of the solutions of the Falkner-Skan equation. In particular, it is shown that \(\lambda^* \geq -0.36\).
scientific article; zbMATH DE number 5318731