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References
Allain G., Small time existence for the Navier-Stokes equations with a free surface. Ecole Polytechnique. Rapport interue, 1984, v. 135, p. 1–24.
Beale J.T., The initial value problem for the Navier-Stokes equations with a free boundary. Comm. Pure Appl. Math., 1980, v. 31, p. 359–392.
Beale J.T., Large-time regularity of viscous surface waves. Arch. Rat. Mech. Anal., 1984, v. 84, p. 307–352.
Bemelmans J., Liquid drops under the influence of gravity and surface tension. Manuscripta Math., 1981, v. 36. No 1, p. 105–123.
Bemelmans J., Free boundary problems for the stationary Navier-Stokes equations. Asterisqué, 1984, No 18, p. 115–123.
Bemelmans J., Equilibrium figures of rotating fluids. Z. angew. Math. und Mech., 1982, v. 62, No 5, p. 273.
Erunova I.B., Solvability of a free boundary problem for two fluids in a container. Vestnik Leningrad. Univ. Math., Mech., Astr., 1986, No 2, p. 9–16 (in Russian).
Ladyzhenskaya O.A., Osmolovskii V.G., The free surface of a layer of fluid over a solid sphere. Vestnik Leningrad. Univ., Math., Mech., Astr., 1976, No 13, p. 25–30 (in Russian).
Maz'ya V.G., Plamenevskii B.A., Stupelis L.I., Three-dimensional problem with a free boundary. Diff equations and their applications. Inst. of Math. and Cybern. Acad. Sci. Lith. SSR, Vilnius, 1979, v. 23, p. 9–153 (in Russian).
Osmolovskii V.G., The free surface of a drop in a symmetric force field. Zapiski Nauchn. Sem. LOMI, 1975, v. 52,p.160–174(in Russian)
Pileckas K., Solvability of a problem of a plane motion of a heavy viscous incompressible fluid with a noncompact free boundary. Diff. equations and their applications. Inst. of Math. and Cybern. Acad. Sci. Lith.SSR, Vilnius, 1981, v. 30, p. 57–96.
Pileckas K., Specovius-Neugebauer M., Solvability of a noncompact free boundary problem for the stationary Navier-Stokes system. Lith. Math. J., I:1989, v. 30, No 3, II:1989, v. 30, No 4 (in Russian).
Pileckas K., On the problem of motion of a heavy viscous incompressible fluid with noncompact free boundary. Lith. Math. J., 1988, v. 29, No 2, p. 315–333 (in Russian).
Pileckas K., The example of nonuniqueness of the solution to a noncompact free boundary problem for the stationary Navier-Stokes s system. Diff. equations and their applications. Inst of Math. and Cybern. Acad. Sci. Lith. SSR, Vilnius, 1988, v. 42, p. 59–64 (in Russian).
Pukhnachov V.V., Plane stationary free boundary problem for the Navier-Stokes equations. Z.Prikl.Meh. i Techn. Fiz., 1972, No 3. p. 91–102 (in Russian).
Pukhnachov V.V., Free boundary problems for Navier-Stokes equations. Doctoral dissertation, Novosibirsk, 1974 (in Russian).
Rivkind V.Ya., Theoretical justification of a method of successive approximations for stationary problems of mechanics a viscous fluid with free surfaces of separation. Zap. Nauchn. Sem. LOMI, 1982, v. 115, p. 228–235 (in Russian).
Rivkind V.Ya., A priori estimates and the method of successive approximations for the motion of a drop. Trudy Math. Inst. Steklov, 1983, v. 159, p. 150–166 (in Russian).
Socolescu D., On one free boundary problem for the stationary Navier-Stokes equations. — Methoden und Verfahren der mathematischen Physik, 1979, c. 18, p. 117–140.
Solonnikov V.A., Solvability of the problem of plane motion of a heavy viscous incompressible capillary liquid partially filling a container. Izv. Akad. Nauk SSSR, 1979, v. 43, p. 203–236 (in Russian), English translation: Math. USSR-Izv., 1980, v. 14, p. 193–221.
Solonnikov V.A., On a free boundary problem for the system of Navier-Stokes equations. Trudy Sem. S.L. Sobolev, 1978, v. 2, p. 127–140 (in Russian).
Solonnikov V.A., Solvability of a three-dimensional boundary value problem with a free surface for the stationary Navier-Stokes system. Partial Diff. Equations, Banach Center Publ., 1983, v. 10, p. 361–403.
Solonnikov V.A., Solvability of the problem of the motion of a viscous incompressible fluid bounded by a free surface. Izv. Akad. Nauk SSSR, Ser. Mat., 1977, v. 41, No 6, p. 1388–1424 (in Russian). English translation: Math. USSR-Izv., 1977, v. 11, No 6, p. 1323–1358.
Solonnikov V.A., On a unsteady motion of an isolated volume of a viscous incompressible fluid, Izv. Akad. Nauk SSSR, Ser. Mat., 1987, v. 51, No 5, p. 1065–1087 (in Russian).
Stűcheli A., Flow development of a highly viscous fluid emerging from a slit onto a plate.-J. Fluid Mech., 1980, v. 97, part 2, p. 321–330.
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Pileckas, K. (1990). Noncompact free boundary problems for the Navier-Stokes equations. In: Heywood, J.G., Masuda, K., Rautmann, R., Solonnikov, V.A. (eds) The Navier-Stokes Equations Theory and Numerical Methods. Lecture Notes in Mathematics, vol 1431. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086055
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