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Blasius Differential Equation

The Blasius differential equation is the third-order nonlinear ordinary differential equation

2y^(''')+yy^('')=0.

This equation arises in the theory of fluid boundary layers (Rosenhead 1963; Schlichting 1979; Tritton 1989, p. 129). The Blasius solution satisfies the boundary conditions y(0)=y^'(0)=0 and y^'(x)->1 as x->infty. Its derivative gives the normalized velocity profile, known as the Blasius profile. This boundary value problem is generally solved numerically, although other solutions of the differential equation are elementary. For example, every linear function y(x)=ax+b satisfies the equation.

See also

Blasius Solution, Boundary Value Problem

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References

Meyer, G. H. Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding. New York: Academic Press, 1973.Rosenhead, L. (Ed.). Laminar Boundary Layers. Oxford, England: Oxford University Press, 1963.Schlichting, H. Boundary Layer Theory, 7th ed. New York: McGraw-Hill, 1979.Tritton, D. J. Physical Fluid Dynamics, 2nd ed. Oxford, England: Clarendon Press, p. 129, 1989.Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 128, 1997.

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Blasius Differential Equation

Cite this as:

Weisstein, Eric W. "Blasius Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BlasiusDifferentialEquation.html

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