ABSTRACT
In the present paper we consider initial-boundary value problem for the Stokes equations
in a bounded convex domain with a smooth boundary S on the basis of the theory of nonstationary hydrodynamic potentials constructed by J.Leray [13] in the case of two and by K.K.Golovkin [2, 5] in the case of three spatial variables. A central role in the theory is played by a special fundamental solution of the Stokes system which permits to obtain an explicit solution of the problem (1.1) with and with
For n=2, it was found by C.W.Oseen [14] in the form of an analytic function of z=x1+ix 2 defined in the half-plane x 2>0 and used by J.Leray as a kernel of his potentials. In the three-dimensional case such a solution was constructed in [2, 15].
