Sharp existence results for the stationary Navier-Stokes problem in three-dimensional exterior domains

The stationary Navier-Stokes problem in a three-dimensional connected exterior domain is formulated in a new functional setting. For the case of a constant but nonzero velocity at infinity and of vanishing boundary fluxes, the problem involves a proper Fredholm operator of index 0. Topological degree arguments provide the existence of solutions and the Sard-S male theorem yields their finiteness in number for generic external forces and boundary velocities.