# Fundamental solutions for stationary Stokes systems with measurable coefficients

## TL;DR

This paper proves the existence and bounds of fundamental solutions for stationary Stokes systems with measurable coefficients in various domains, assuming local Hölder continuity of solutions, extending classical results to less regular coefficients.

## Contribution

It establishes the fundamental solution's existence and bounds for Stokes systems with measurable coefficients in unbounded domains, under minimal regularity assumptions.

## Key findings

- Existence of fundamental solutions in whole space and unbounded domains
- Pointwise bounds for the fundamental solutions
- Extension to domains like half space and exterior domains

## Abstract

We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $\mathbb{R}^d$, $d \ge 3$, under the assumption that weak solutions of the system are locally H\"older continuous. We also discuss the existence and the pointwise bound of the Green function for the Stokes system with measurable coefficients on $\Omega$, where $\Omega$ is an unbounded domain such that the divergence equation is solvable. Such a domain includes, for example, half space and an exterior domain.