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**There seems to be something wrong with the LaTeX**

This seems like an absolutely trite question, but I can't seem to figure it out.

Suppose you had a boundary-layer problem, say at x = 0. Suppose the first term of the outer solution, valid away from x = 0 was [tex]\sim x^{1/4}[/tex]. Suppose that the boundary layer was of thickness [tex]x = O(\epsilon)[/tex].

Suppose that you have solved for the inner solution near x = 0. What would be the required matching condition?

So in this example, we would re-scale [tex]x = \epsilon X[/tex]. Then wouldn't the inner solution need to behave like, [tex]y \sim \epsilon^{1/4} X^{1/4}[/tex] as [tex]X \to \infty[/tex]? But this doesn't seem possible, since we can't allow the inner solution to blow up. What is the correct matching condition as [tex]X \to \infty[/tex]?

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