Spatial behavior of solutions to the time periodic Stokes system in a three dimensional layer

Starting from solutions to the Dirichlet boundary value problem for the time-periodic Stokes system in a 3D-layer the subject of this paper is the asymptotic behavior of the velocity field and pressure for large x. For suitably decaying data the full asymptotic decomposition of the solution is constructed for large x and justified by estimates for the remainder. The decay conditions for the data and the estimates for the remainder are formulated in weighted Sobolev spaces with power-type weights.