Geodesic
Estimates of solutions of a~general initial-boundary value problem for linearized nonstationary Navier--Stokes system in the half-space
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 147-173

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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. 
@article{ZNSL_1979_84_a12,
     author = {I. Sh. Mogilevskii},
     title = {Estimates of solutions of a~general initial-boundary value problem for linearized nonstationary {Navier--Stokes} system in the half-space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {147--173},
     publisher = {mathdoc},
     volume = {84},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a12/}
}
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I. Sh. Mogilevskii. Estimates of solutions of a~general initial-boundary value problem for linearized nonstationary Navier--Stokes system in the half-space. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 11, Tome 84 (1979), pp. 147-173. http://geodesic.mathdoc.fr/item/ZNSL_1979_84_a12/