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 suitable function spaces.