Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity

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1. [1] F. Abergel - J.L. Bona, A mathematical theory for viscous free-surface flows over a perturbed plane, Arch. Rational Mech. Anal., 118 (1992), pp. 71-93. Zbl0765.76024MR1151927
2. [2] R.A. Adams, Sobolev Spaces, Academic Press, New York, San Francisco, London (1975). Zbl0314.46030MR450957
3. [3] C.J. Amick, Steady solutions of the Navier-Stokes equations in unbounded channels and pipes, Ann. Scuola Norm. Sup. Pisa, 4 (1977), pp. 473-513. Zbl0367.76027MR510120
4. [4] C.J. Amick, Properties of steady Navier-Stokes solutions for certain unbounded channels and pipes, Nonlinear analisys, Theory, Meth., Appl., 2 (1978), pp. 689-720. Zbl0389.76026MR512162
5. [5] C.J. Amick - L. E. FRAENKEL, Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types, Acta Math., 144 (1980), pp. 81-152. Zbl0439.76018MR558092
6. [6] W. Borchers - K. Pileckas, Existence, uniqueness and asymptotics of steady jets, Arch. Rational Mech. Anal., 120 (1992), pp. 1-49. Zbl0772.76021MR1182406
7. [7] W. Borchers - G.P. Galdi - K. Pileckas, On the uniqueness of Leray-Hopf solutions for the flow through an aperture, Arch. Rational Mech. Anal., 122 (1993), pp. 19-33. Zbl0781.35050MR1207239
8. [8] G.P. Galdi, AnIntroduction to the Mathematical Theory of the Navier-Stokes Equations, Springer Tracts in Natural Philosophy, 38, 39 (1994). Zbl0949.35005MR1284205
9. [9] L.V. Kapitanskii - K. Pileckas, On spaces of solenoidal vector fields and boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries, Trudy Mat. Inst. Steklov, 159 (1983), pp. 5-36; English transl.: Proc. Math. Inst. Steklov, 159, issue 2 (1984), pp. 3-34. Zbl0585.76038MR720205
10. [10] O.A. Ladyzhenskaya, TheMathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, London, Paris (1969). Zbl0184.52603MR254401
11. [11] O.A. Ladyzhenskaya - V.A. Solonnnikov, On some problems of vector analysis and generalized formulations of boundary value problems for the Navier-Stokes equations, Zapiski Nauchn. Sem.LOMI, 59 (1976), pp. 81-116; English transl.: J. Sov. Math., 10, No. 2 (1978), pp. 257-285. Zbl0388.35061MR467031
12. [12] O.A. Ladyzhenskaya - V.A. Solonnnikov, On the solvability of boundary value problems for the Navier-Stokes equations in regions with noncompact boundaries, Vestnik Leningrad. Univ. (Ser. Mat. Mekh. Astr. vyp. 3), 13 (1977), pp. 39-47; English transl.: Vestnik Leningrad Univ. Math., 10 (1982), pp. 271-280. Zbl0494.35078
13. [13] O.A. Ladyzhenskaya - V.A. Solonnnikov, Determination of the solutions of boundary value problems for stationary Stokes and Navier-Stokes equations having an unbounded Dirichlet integral, Zapiski Nauchn. Sem.LOMI, 96 (1980), pp. 117-160; English transl.: J. Sov. Math., 21, No. 5 (1983), pp. 728-761. Zbl0509.35066MR579479
14. [14] L.D. Landau - E.M. Lifschitz, Hydromechanik, Akademie-Verlag, Berlin (1971). 
15. [15] V.N. Maslennikova - M.E. Bogovskii, Sobolev spaces of solenoidal vector fields, Sibirsk. Mat. Zh., 22 (1981), pp. 91-118; English transl.: Siberian Math. J., 22 (1982), pp. 399-420. Zbl0512.46036MR621465
16. [16] S.A. Nazarov - K. Pileckas, On the behaviour of solutions of the Stokes and Navier-Stokes systems in domains with periodically varying section, Trudy Mat. Inst. Steklov, 159 (1983), pp. 137-149; English transl.: Proc. Math. Inst. Steklov, 159, issue 2 (1984), pp. 141-154. Zbl0554.76032MR1770190
17. [17] S.A. Nazarov - K. Pileckas, On noncompact free boundary problems for the plane stationary Navier-Stokes equations, J. Reine Angewandte Math., 438 (1993), pp. 103-141. Zbl0767.35111MR1215650
18. [18] K. Pileckas, Three-dimensional solenoidal vectors, Zapiski Nauchn. Sem.LOMI, 96 (1980), pp. 237-239; English transl.: J. Sov. Math., 21 (1983), pp. 821-823. Zbl0509.46021
19. [19] K. Pileckas, On the solvability of certain problem of a plane motion of viscous incompressible liquid with a noncompact free boundary, Zapiski Nauchn. Sem.LOMI, 110 (1981), pp. 174-179; English transl.: J. Sov. Math., 25, No. 1 (1984), pp. 927-931. Zbl0531.76037MR643983
20. [20] K. Pileckas, Existence of solutions for the Navier-Stokes equations having an infinite dissipation of energy, in a class of domains with noncompact boundaries, Zapiski Nauchn. Sem.LOMI, 110 (1981), pp. 180-202; English transl.: J. Sov. Math., 25, No. 1 (1984), pp. 932-947. Zbl0531.76038MR643984
21. [21] K. Pileckas, Solvability of a problem of a plane motion of viscous fluid with noncompact boundary, Differential Equations and their Application, Vilnius, 30 (1981), pp. 57-96 (in Russian). Zbl0504.76032
22. [22] K. Pileckas, On spaces of solenoidal vectors, Trudy Mat. Inst. Steklov, 159 (1983), pp. 137-149; English transl.: Proc. Math. Inst. Steklov, 159, issue 2 (1984), pp. 141-154. Zbl0541.35008MR720212
23. [23] K. Pileckas, On the problem of motion of heavy viscous incompressible fluid with noncompact free boundary, Litovskii Mat. Sb., 28 (1988), pp. 315-333; English transl.: Lithuanian Math. J., 28, No. 2 (1988). Zbl0657.76030MR966116
24. *[24] K. Pileckas, On plane motion of a viscous incompressible cappilary liquid with a noncompact free boundary, Arch. Mech., 41, No. 2-3 (1989), pp. 329-342. Zbl0717.76040MR1083808
25. [25] K. Pileckas - V.A. Solonnikov, On stationary Stokes and Navier-Stokes systems in an open infinite channel. I., Litovskii Mat. Sb., 29, No. 1 (1989), pp. 90-108; English transl.: Lithuanian Math. J., 29, No. 1 (1989); II., Litovskii Mat. Sb., 29, No. 2 (1989), pp. 347-367. English transl.: Lithuanian Math. J., 29, No. 2 (1989). Zbl0714.35067
26. [26] K. Pileckas - M. Specovius-Neugebauer, Solvability of a noncompact free boundary problem for the stationary Navier-Stokes system. I., Litovskii Mat. Sb., 29, No. 3 (1989), pp. 532-547. English transl.: Lithuanian Math. J., 29, No. 3 (1989); II., Litovskii Mat. Sb., 29, No. 4 (1989), pp. 773-784 (in Russian). Zbl0727.35108
27. [27] K. Pileckas, Weighted Lq-solvability for the steady Stokes system in domains with noncompact boundaries, Mathematical Models and Methods in Applied Sciences, 6, No. 1 (1996), pp. 97-136. Zbl0859.35092MR1373339
28. [28] K. Pileckas, Classical solvability and uniform estimates for the steady Stokes system in domains with noncompact boundaries, Mathematical Models and Methods in Applied Sciences, 6, No. 2 (1996), pp. 149-167. Zbl0870.35079MR1380694
29. [29] V.A. Solonnikov - K. Pileckas, Certain spaces of solenoidal vectors and the solvability of the boundary value problem for the Navier-Stokes system of equations in domains with noncompact boundaries, Zapiski Nauchn. Sem.LOMI, 73 (1977), pp. 136-151; English transl.: J. Sov. Math., 34, No. 6 (1986), pp. 2101-2111. Zbl0612.35111MR513173
30. [30] V.A. Solonnikov, On the solvability of boundary and initial-boundary value problems for the Navier-Stokes system in domains with noncompact boundaries, Pacific J. Math., 93, No. 2 (1981), pp. 443-458. Zbl0413.35062MR623575
31. [31] V.A. Solonnikov, On solutions of stationary Navier-Stokes equations with an infinite Dirichlet integral, Zapiski Nauchn. Sem.LOMI, 115 (1982), pp. 257-263; English transl.: J. Sov. Math., 28, No. 5 (1985), pp. 792-799. Zbl0561.76045MR660087
32. [32] V.A. Solonnikov, Stokes and Navier-Stokes equations in domains with noncompact boundaries, College de France Seminar, 4 (1983), pp. 240-349. Zbl0547.35102MR716521
33. [33] V.A. Solonnikov, Boundary and initial-boundary value problems for the Navier-Stokes equations in domains with noncompact boundaries, Math. Topics in Fluid Mechanics, Pitman Research Notes in Mathematics Series, 274 (eds. J. F. Rodriques, A. Sequeira) (1991), pp. 117-162. Zbl0794.76025MR1204926
34. [34] V.A. Solonnikov - V.E. Shchadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov, 125 (1973), pp. 196-210; English transl.: Proc. Mat. Inst. Steklov, 125 (1973), pp. 186-199. Zbl0313.35063MR364910
35. [35] R. Temam, Navier-Stokes Equations, North-Holland Pub. Co., Amsterdam, New York, Tokyo (1977). Zbl0383.35057MR769654

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