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A two-point boundary value problem in the interval (e, eo), e > 0 is studied. The problem contains additional parameters a -> 0,/3 -> 0, 0-< U< oo, k real. It was originally proposed by Lagerstrom as a model for viscous flow at low Reynolds numbers. A related initial value problem is transformed into an integral equation which is shown to have a unique solution by a pincer method. The integral representation is used for a simple proof of the existence of a solution of the boundary value problem for a > 0; for a 0 an explicit construction shows that no solution exists unless k> 1. A special method is used to show uniqueness. For e $ 0, k => 1, various results had previously been obtained by the method of matched asymptotic expansions. Examples of these results are verified rigorously using the integral representation. For k < 1, the problem is shown not to be a layer-type problem, a fact previously demonstrated explicitly for k 0. If k is an integer => 0 the intuitive understanding of the problem is aided by regarding it as spherically symmetric in k + dimensions. In the present study, however, k may be any real number, even negative.

Proof of Some Asymptotic Results for a Model Equation for Low Reynolds Number Flow