Geodesic
The stationary solutions to the two-dimensional Navier--Stokes equation for large fluxes
Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 61-69.

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We prove some results concerning with solvability of stationary homogeneous incompressible 2D Navier–Stokes equations with non-zero fluxes. 
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A. A. Illarionov; L. V. Illarionova. The stationary solutions to the two-dimensional Navier--Stokes equation for large fluxes. Dalʹnevostočnyj matematičeskij žurnal, Tome 15 (2015) no. 1, pp. 61-69. http://geodesic.mathdoc.fr/item/DVMG_2015_15_1_a5/

[1] J. Leray, “Etude de diverses équations, integrales non lineaire et de queques problemes que posent l'Hydrodynamique”, J. Math. Pures Appl., 35:12 (1933), 1–82

[2] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, M., 1970 | MR

[3] V. I. Yudovich, “Eleven great problems of mathematical hydrodynamics”, Mosc. Math. J., 3:2 (2003), 711–737 | MR | Zbl

[4] A. Takeshita, “A remark on Leray's inequality”, Pacific J. Math., 157:1 (1993), 151–158 | DOI | MR | Zbl

[5] A. A. Illarionov, “O vozmozhnosti obobscheniya lemmy Khopfa na sluchai uravnenii Nave–Stoksa s nenulevymi potokami”, Sib. matem. zhurn, 50:4 (2009), 831–835 | MR | Zbl

[6] C. J. Amick, “Existence of solutions to the nonhomogeneous steady Navier – Stokes equations”, Indiana Univ. Math. J., 33:6 (1984), 817–830 | DOI | MR | Zbl

[7] L. I. Sazonov, “O suschestvovanie statsionarnogo simmetrichnogo resheniya dvumernoi zadachi o protekanii zhidkosti”, Matem. zametki, 54:6 (1993) | MR | Zbl

[8] H. Fujita, “On the stationary solutions to Navier-Stokes equations in simmetric plane domains under general outflow conditions”, Proceeding of International Conference on Navier – Stokes equations, Theory and Numerical methods, 1997, Varenna, Italy. Pitman Research Notes in Math. 388, 16–30 | MR | Zbl

[9] V. V. Pukhnachev, “Viscous flows in domains with a multiply connected boundary”, New directions in mathematical fluid mechanics, Adv. Math. Fluid Mech., Birkhauser Verlag, Basel,, 2010, 333–348 | MR | Zbl

[10] M. V. Korobkov, K. Pileckas, R. Russo, “On the Flux Problem in the Theory of Steady Navier – Stokes Equations with Nonhomogeneous Boundary Conditions”, Arch. Rational Mech. Anal., 207 (2013), 185–213 | DOI | MR | Zbl

[11] H. Fujita, H. Morimoto, “A remark on the existence of steady Navier – Stokes flow with non-vanishing outflow conditions”, Gakuto International Series in Math. Science and Appl., Nonlinear Waves,, 10 (1997), 53–61 | MR | Zbl

[12] H. Morimoto, “Note on the boundary value problem for the Navier–Stokes equations in 2–D domain with general outfllow condition (in Japanese)”, Memoirs of the Institute of Science and Technology, Meiji University, 35 (1997), 95–102

[13] H. Morimoto, “General outflow condition for Navier–Stokes system”, In “Recent Topics on Mathematical Theory of Viscous Incompressible fluid”, Lectures Notes in Num. Appl. Anal., 16 (1998), 209–224 | MR | Zbl

[14] A. Russo, G. Starita, “On the existence of steady-state solutions to the Navier–Stokes system for large fluxes”, Ann. Scuola Norm. Sup. Pisa, 7 (2008), 171–180 | MR | Zbl

[15] V. V. Ragulin, “K zadache o protekanii vyazkoi zhidkosti skvoz ogranichennuyu oblast pri zadannom perepade davleniya ili napora”, Dinamika sploshnoi sredy., 1976, no. 27, 78–92 | MR

[16] C. Bègue, C. Conca, F. Murat, O. Pironneau, “A nouveau sur les équations de Stokes et de Navier-Stokes avec des conditions aux limites sur la pression”, C. R. Acad. Sc. Paris. Série I., 304:2 (1987), 23–28 | MR

[17] A. Yu. Chebotarev, “Subdifferentsialnye kraevye zadachi dlya statsionarnykh uravnenii Nave – Stoksa”, Differents. uravneniya, 28:8 (1992), 1443–1450 | MR | Zbl

[18] C. Conca, F. Murat, O. Pironneau, “The Stokes and Navier-Stokes equation with boundary conditions involving the pressure”, Japan J. Math., 20:2 (1994), 279–318 | MR | Zbl

[19] A. A. Illarionov, A. Yu. Chebotarev, “O razreshimosti smeshannoi kraevoi zadachi dlya statsionarnykh uravnenii Nave – Stoksa”, Differents. uravneniya, 37:5 (2001), 689–695 | MR | Zbl

[20] A. A. Illarionov, “O razreshimosti kraevykh zadach dlya statsionarnykh uravnenii Nave – Stoksa”, Dalnevostochnyi matem. zhurn., 2:1 (2001), 16–36

[21] A. A. Illarionov, “Suschestvovanie statsionarnogo simmetrichnogo resheniya dvumernykh uravnenii Nave – Stoksa s zadannym naporom i nenulevymi potokami”, Differents. uravneniya, 45:8 (2009), 1116–1125 | MR | Zbl