A fundamental solution to the time-periodic Stokes equations

TL;DR

This paper introduces and analyzes a fundamental solution for the time-periodic Stokes equations in multiple dimensions, providing key estimates and integrability properties essential for understanding these equations.

Contribution

It presents the first explicit fundamental solution for the time-periodic Stokes equations and analyzes its mathematical properties.

Findings

Established integrability of the fundamental solution

Derived pointwise estimates for the solution

Provided a rigorous analysis of the solution's properties

Abstract

The concept of a fundamental solution to the time-periodic Stokes equations in dimension $n\geq 2$ is introduced. A fundamental solution is then identified and analyzed. Integrability and pointwise estimates are established.