Abstract
In a bounded domain of the space R n (n=2 or 3) we consider the initialand boundary-value problem regarding the determination of the velocity vector of the fluid, the pressure, and the density from the system of Navier-Stokes equation and the continuity equations, as well as from the initial conditions for the velocity and from the adherence boundary conditions. It is proved that the three-dimensional problem is uniquely solvable on some finite time interval and, in the case of a small initial velocity vector and a small volume force, also on an infinite interval; however, the two-dimensional problem is uniquely solvable for all t⩾0 without any smallness restrictions.
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