Abstract

In this paper we deal with the stationary Navier-Stokes problem in a domain $\Omega $ with compact Lipschitz boundary $\partial \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 \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