Geodesic
On~the transient motion of an isolated volume of viscous incompressible fluid
Izvestiya. Mathematics , Tome 31 (1988) no. 2, pp. 381-405

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Solvability locally in time is proved for a free-boundary problem describing the evolution of a finite mass of viscous incompressible fluid in $\mathbf R^n$, $n=2,3$, without taking surface tension into account. Sufficient conditions for the extension of a solution to the infinite time interval $t>0$ are given. A solution is obtained in the space $W_p^{2,1}$ with $p>n$. Bibliography: 19 titles. 
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     author = {V. A. Solonnikov},
     title = {On~the transient motion of an isolated volume of viscous incompressible fluid},
     journal = {Izvestiya. Mathematics },
     pages = {381--405},
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     volume = {31},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_31_2_a6/}
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V. A. Solonnikov. On~the transient motion of an isolated volume of viscous incompressible fluid. Izvestiya. Mathematics , Tome 31 (1988) no. 2, pp. 381-405. http://geodesic.mathdoc.fr/item/IM2_1988_31_2_a6/