Geodesic
On a~steady three-dimensional noncompact free boundary value problem for the Navier--Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 134-164

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A steady three-dimensional flow of a viscous incompressible fluid with a noncompact free boundary above a fixed unbounded bottom is studied. It is assumed that the motion of the fluid is generated by sources and sinks situated in a bounded part of the bottom and having zero total flux. The existence for small data of the unique solution to this problem is proved and the asymptotics of the solution is constructed. 
@article{ZNSL_2003_306_a6,
     author = {K. I. Pileckas and L. Zaleskis},
     title = {On a~steady three-dimensional noncompact free boundary value  problem for the {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {134--164},
     publisher = {mathdoc},
     volume = {306},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a6/}
}
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K. I. Pileckas; L. Zaleskis. On a~steady three-dimensional noncompact free boundary value  problem for the Navier--Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 34, Tome 306 (2003), pp. 134-164. http://geodesic.mathdoc.fr/item/ZNSL_2003_306_a6/