## 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.

### MSC:

 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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### References:

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