A challenging nonlinear problem for numerical techniques. (English) Zbl 1071.65112

Summary: We show that a nonlinear boundary-value problem describing Blasius viscous flow of a kind of non-Newtonian fluid has an infinite number of explicit analytic solutions. These solutions are rather sensitive to the second-order derivative at the boundary, and the difference of the second derivatives of two obviously different solutions might be less than \(10^{-1000}\). Therefore, it seems impossible to find out all of these solutions by means of current numerical methods. Thus, this nonlinear problem might become a challenge to current numerical techniques.


65L10 Numerical solution of boundary value problems involving ordinary differential equations
76A05 Non-Newtonian fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
34B15 Nonlinear boundary value problems for ordinary differential equations
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