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The Blasius function in the complex plane. (English) Zbl 0980.34053

This paper is devoted to the unique solution to the following nonlinear boundary value problem

$2{f}_{xxx}+f{f}_{xx}=0$

with the conditions $f\left(0\right)={f}_{x}\left(0\right)=0$ and ${f}_{x}\left(\infty \right)=1$.

The author gives a very interesting overview on the state of art of this solution which is called Blasius function. Aside to algebraic and analytic properties the reader can find essential numerical implementations and an analysis of problems with this. The image of the Blasius function in the complex plane is also studied sufficiently detailed.

MSC:
 34E05 Asymptotic expansions (ODE) 34B15 Nonlinear boundary value problems for ODE 76D10 Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids) 34M05 Entire and meromorphic solutions (ODE)
Blasius function