1 Introduction

Until the beginning of the twentieth century, analytical solutions of steady fluid flows were generally known for two typical situations. One of these was that of parallel viscous flows and low Reynolds number flows, in which the nonlinear advective terms were zero and the balance of forces was that between the pressure and the viscous forces. The second type of solution was that of inviscid flows around bodies of various shapes, in which the balanceof forces was that between the inertia and pressure forces. Although the equations of motion are nonlinear in this case, the velocity field can be determined by solving the linear Laplace equation. These irrotational solutions predicted pressure forces on a streamlined body that agreed surprisingly well with experimental data for flow of fluids of small viscosity. However, these solutions also predicted a zero drag force and a nonzero tangential velocity at the surface, features that did not agree with the experiments.

In 1905 Ludwig Prandtl, an engineer by profession and therefore motivated to find realistic fields near bodies of various shapes, first hypothesized that, for small viscosity, the viscous forces are negligible everywhere except close to the solid bound-aries where the no-slip condition had to be satisfied. The thickness of these boundary layers approaches zero as the viscosity goes to zero. Prandtl's hypothesis reconciled two rather contradictory facts. On one hand he supported the intuitive idea that the effects of viscosity are indeed negligible in most of the flow field if ? is...