Geodesic
On an unsteady flow of a~finite mass of a~liquid bounded by a~free surface
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 137-157

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It is proved that the intial-value problem for the Navier–Stokes equations describing the motion of a viscous incompressible liquid bounded by a free surface has the unique solution in an infinite time interval $t>0$, if the domain occupied by the biquid is close to a ball and the velocity vector field is small at the initial moment of time. 
@article{ZNSL_1986_152_a11,
     author = {V. A. Solonnikov},
     title = {On an unsteady flow of a~finite mass of a~liquid bounded by a~free surface},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {137--157},
     publisher = {mathdoc},
     volume = {152},
     year = {1986},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a11/}
}
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V. A. Solonnikov. On an unsteady flow of a~finite mass of a~liquid bounded by a~free surface. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 18, Tome 152 (1986), pp. 137-157. http://geodesic.mathdoc.fr/item/ZNSL_1986_152_a11/