On the transient motion of an isolated volume of viscous incompressible fluid

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 $p>n$.
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