On the existence of steady-state solutions to the Navier-Stokes system for large fluxes

In this paper we deal with the stationary Navier-Stokes problem in a domain Omega with compact Lipschitz boundary partial derivative Omega and datum a in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of partial derivative Omega, with possible countable exceptional set, provided a is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for Omega bounded.