On the existence of steady-state solutions to the Navier-Stokes system for large fluxes
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 1, pp. 171-180.

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.

Classification : 76D05,  31B10,  35Q30,  42B20
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author = {Russo, Antonio and Starita, Giulio},
title = {On the existence of steady-state solutions to the {Navier-Stokes} system for large fluxes},
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Russo, Antonio; Starita, Giulio. On the existence of steady-state solutions to the Navier-Stokes system for large fluxes. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 7 (2008) no. 1, pp. 171-180. http://archive.numdam.org/item/ASNSP_2008_5_7_1_171_0/

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