Estimates of solutions of a general initial-boundary value problem for linearized nonstationary Navier–Stokes system in the half-space

In the half-space $x_3>0$ the initial-boundary value problem for the Stokes system in which the boundary conditions are given by means of a 3x4-matrix differential operator is considered. It is proved that under certain restrictions on this operafor the coercive a-priori estimates in the norm $W_p^{2l,l}$ for the solution are valid.