Estimates for Green functions of Stokes systems in two dimensional domains

TL;DR

This paper establishes the existence and bounds of Green functions for stationary Stokes systems with measurable coefficients in 2D domains, including derivative bounds under certain regularity conditions.

Contribution

It provides new proofs for Green function existence and bounds in 2D Stokes systems with measurable coefficients, extending previous results to include derivative estimates.

Findings

Existence of Green functions in 2D Stokes systems.

Pointwise bounds for Green functions and their derivatives.

Results applicable under regularity assumptions on coefficients.

Abstract

We prove the existence and pointwise bounds of the Green functions for stationary Stokes systems with measurable coefficients in two dimensional domains. We also establish pointwise bounds of the derivatives of the Green functions under a regularity assumption on the $L_1$-mean oscillations of the coefficients.