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Stationary Stokes and Navier-Stokes systems in an infinite open channel. I

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Literature Cited

  1. O. A. Ladyzhenskaya and V. A. Solonnikov, “Finding solutions of boundary problems for stationary Stokes and Navier-Stokes equations having unbounded Dirichlet integral,” J. Sov. Math.,21, No. 5 (1983).

  2. V. A. Solonnikov, “Stokes and Navier-Stokes equations in domains with noncompact boundaries,” College de France Seminar,4, 240–349 (1983).

    Google Scholar 

  3. V. A. Solonnikov, “Solvability of the three-dimensional problem with free boundary for the stationary system of Navier-Stokes equations,” J. Sov. Math.,21, No. 3 (1983).

  4. V. A. Solonnikov, “Solvability of a three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system,” Partial Diff. Equations, Banach Center Publ.,10, 361–403 (1983).

    Google Scholar 

  5. V. A. Solonnikov, “On the Stokes equation in domains with nonsmooth boundaries and on viscous incompressible flow with a free surface,” College de France Seminar,3, 340–423 (1980/1981).

    Google Scholar 

  6. V. G. Maz'ya, B. A. Plamenevskii, and L. I. Stupyalis, “Three-dimensional problem on steady state motion of a fluid with free surface,” Differents. Uravn. Primen.,23, 9–154 (1980).

    Google Scholar 

  7. V. G. Maz'ya and B. A. Plamenevskii, “Estimates in Lp and in Hölder classes and the Miranda-Agmon maximum principle for solutions of elliptic boundary problems in domains with singular points on the boundary,” Math. Nachr.,81, 25–82 (1978).

    Google Scholar 

  8. K. I. Piletskas, “Solvability of a problem on planar motion of a viscous incompressible fluid with free noncompact boundary,” Differents. Uravn. Primen.,30, 57–95 (1981).

    Google Scholar 

  9. V. A. Solonnikov, “Solvability of problem on the flow of a viscous incompressible fluid in an infinite open reservoir,” Trudy Mat. Inst. Akad. Nauk SSSR,179 (1987).

  10. K. I. Piletskas, “Flow of a turbid viscous incompressible fluid with free noncompact boundary,” Liet. Mat. Rinkinys,28, No. 2, 315–333 (1988).

    Google Scholar 

  11. V. A. Kondrat'ev, “Boundary problems for elliptic equations in domains with conical or corner points,” Trudy Mosk. Mat. Obshch.,16, 209–292 (1967).

    Google Scholar 

  12. V. A. Kondrat'ev, “Smoothness of solutions of the Dirichlet problem for second-order elliptic equations in a piecewise-smooth domain,” Differents. Uravn.,6, No. 10, 1831–1843 (1970).

    Google Scholar 

  13. V. G. Maz'ya and B. A. Plamenevskii, “Lp-estimates of solutions of elliptic boundary problems in domains with edges,” Trudy Mosk. Mat. Obshch.,37, 49–93 (1978).

    Google Scholar 

  14. V. G. Maz'ya and B. A. Plamenevskii, “Coefficients in asymptotic solutions of elliptic boundary problems near conical points,” Dokl. Akad. Nauk SSSR,219, No. 2, 286–289 (1974).

    Google Scholar 

  15. V. A. Solonnikov, “Solvability of a problem on the planar motion of a turbid viscous incompressible capillary fluid partially filling a vessel,” Izv. Akad. Nauk SSSR, Ser. Mat.,43, No. 1, 203–236 (1979).

    Google Scholar 

  16. V. A. Solonnikov, “On the solvability of boundary and initial-boundary-value problems for the Navier-Stokes system in domains with noncompact boundaries,” Pac. J. Math.,93, No. 2, 443–458 (1981).

    Google Scholar 

  17. O. A. Ladyzhenskaya and V. A. Solonnikov, “Problems of vector analysis and generalized formulations of boundary problems for the Navier-Stokes equations,” J. Sov. Math.,10, No. 2 (1978).

  18. O. A. Ladyzhenskaya and V. A. Solonnikov, “Solvability of boundary and initial-boundary problems for the Navier-Stokes equations in domains with noncompact boundaries,” Vestn. Leningr. Univ.,3, No. 13, 39–47 (1977).

    Google Scholar 

  19. V. A. Solonnikov and K. I. Piletskas, “Spaces of solenoidal vectors and the solvability of a boundary problem for the system of Navier-Stokes equations in domains with noncompact boundaries,” J. Sov. Math.,34, No. 6 (1986).

  20. K. I. Piletskas, “Spaces of solenoidal vectors,” Trudy Mat. Inst. Akad. Nauk SSSR,159, 137–149 (1982).

    Google Scholar 

  21. V. A. Solonnikov and V. E. Shchadilov, “A boundary problem for the stationary system of Navier-Stokes equations,” Trudy Mat. Inst. Akad. Nauk SSSR,125, 196–210 (1973).

    Google Scholar 

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Institute of Mathematics and Cybernetics, Academy of Sciences of the Lithuanian SSR. Leningrad Division of the Mathematical Institute, Academy of Sciences of the USSR. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 29, No. 1, pp. 90–108, January–March, 1989.

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Pileckas, K., Solonnikov, V. Stationary Stokes and Navier-Stokes systems in an infinite open channel. I. Lith Math J 29, 34–47 (1989). https://doi.org/10.1007/BF00966498

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