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

TL;DR

This paper studies the time-periodic Stokes equations in a half-space with inhomogeneous boundary conditions, establishing maximal regularity using Fourier multiplier techniques and decomposing solutions into steady and oscillatory parts.

Contribution

It introduces a Fourier multiplier-based method to analyze the regularity of solutions and decomposes solutions into steady and oscillatory components for optimal function space identification.

Findings

Maximal regularity in a time-periodic Lp setting is proven.

Solution decomposition into steady-state and oscillatory parts is achieved.

Optimal function spaces for solutions are identified.

Abstract

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.