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

Abstract

In this paper we deal with the stationary Navier–Stokes problem in a domain Ω with compact, nonconnected Lipschitz boundary ∂Ω and datum a in Lebesgues spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of ∂Ω, whitin a countable set, provided a is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for Ω bounded.