Solvability of a certain problem on the plane motion of two viscous incompressible fluids with free noncompact boundaries
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 146-153

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The solvability of a two-dimentional boundary-value problem for the Navier–Stokes system, which describes the steady (partially common) motion of two heavy viscous non-compressible capillary liquids with non-compact free boundaries is proved.
@article{ZNSL_1987_163_a12,
     author = {Yu. Sokolowski},
     title = {Solvability of a certain problem on the plane motion of two viscous incompressible fluids with free noncompact boundaries},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {146--153},
     publisher = {mathdoc},
     volume = {163},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a12/}
}
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Yu. Sokolowski. Solvability of a certain problem on the plane motion of two viscous incompressible fluids with free noncompact boundaries. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 19, Tome 163 (1987), pp. 146-153. http://geodesic.mathdoc.fr/item/ZNSL_1987_163_a12/