The vanishing viscosity limit for incompressible flows in the presence of boundaries is a well-known open problem. In this talk we will discuss the vanishing viscosity limit in a domain which is expanding to fill all of R^N, N= 2,3. This is a joint work with Jim Kelliher (UC Riverside) and Milton Lopes Filho (UNICAMP) which is an outgrowth of work on singular domain perturbations and the vanishing viscosity limit.