Time-periodic Stokes equations with inhomogeneous Dirichlet boundary conditions in a half-space

The time-periodic Stokes problem in a half-space with fully inhomogeneous right-hand side is investigated. Maximal regularity in a time-periodic Lp setting is established. A method based on Fourier multipliers is employed that leads to a decomposition of the solution into a steady-state and a purely oscillatory part in order to identify the optimal function spaces.