On the exterior three-dimensional slow viscous flow problem

Some recent results concerning the validity of the method of matched asymptotic expansions for treating the stationary flow of an incompressible viscous fluid past an isolated rigid body in three-dimensional space and in two dimensions are summarized. The flow is formulated as an exterior boundary value problem for the velocity and pressure satisfying the Navier-Stokes equations in dimensionless form. The total force exerted on the obstacle by the fluid is analyzed. A perturbation procedure is applied to the problem to obtain a sequence of boundary value problems for the velocity and pressure by equating like powers of Reynolds number. A linearization for the flow about infinity is also summarized, and theorems are given and discussed.