Proudman and Pearson (1957) and other key references.

However, the MAE approach, despite its immense power and diversity of expanding applications, does not give a clean resolution of the original difficulty in that such methods rely essentially on computing and then matching solutions to the problem defined on two regions: close to the cylinder and far from the cylinder. The purpose of this paper is to address the problem of finding [*global*]{} solutions for the low Reynolds number limit, i.e. to resolve the original paradox. There are, of course, other approaches to the paradox. Recently, Villas Boas [@mario] has considered the problem from a three-dimensional perspective and points out that there is then no paradox.

Viscous incompressible flow in 2D
=================================

A large class of fluids can be characterized by their density, $\rho$, a scalar field not presumed to be constant, and their dynamic viscosity $\mu$. The flow is characterized by a velocity vector field $\underline{v}$, and an associated scalar pressure field $p$. Conservation of mass is expressed by the continuity equation $$\frac{\partial \rho}{\partial t} + \del.(\rho \vvec) = 0$$ and the conservation of momentum is expressed by the Navier-Stokes equations[^3] $$\rho(\frac{\partial \vvec}{\partial t} + \vvec.\del \vvec) = -\del p 