Geodesic
Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container
Izvestiya. Mathematics, Tome 14 (1980) no. 1, pp. 193-221 
V. A. Solonnikov. Solvability of a problem on the plane motion of a heavy viscous incompressible capillary liquid partially filling a container. Izvestiya. Mathematics, Tome 14 (1980) no. 1, pp. 193-221. http://geodesic.mathdoc.fr/item/IM2_1980_14_1_a8/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The solvability of a plane stationary boundary value problem for the Navier–Stokes system of equations describing the motion of a viscous incompressible capillary liquid with a free surface is proved. It is assumed that the free surface maintains contact with the wall of the container holding the liquid. Bibliography: 21 titles.

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[15] Ladyzhenskaya O. A., Solonnikov V. A., “O nekotorykh zadachakh vektornogo analiza i obobschennykh postanovkakh kraevykh zadach dlya uravnenii Nave–Stoksa”, Zap. nauchn. seminarov Leningr. otd. Matem. in-ta im. V. A. Steklova AN SSSR, 59, 1976, 81–116 | Zbl

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[21] Ladyzhenskaya O. A., Solonnikov V. A., “Ob odnoznachnoi razreshimosti kraevoi zadachi dlya vyazkikh neszhimaemykh neodnorodnykh zhidkostei”, Zap. nauchn. seminarov Leningr. otd. Matem. in-ta im. V. A. Steklova AN SSSR, 52, 1975, 52–109 | Zbl