Wolff Type Potential Estimates for Stationary Stokes Systems with Dini-BMO Coefficients

TL;DR

This paper establishes pointwise gradient estimates for stationary Stokes systems with Dini-BMO coefficients using Wolff potential techniques, providing bounds without additional regularity assumptions on the coefficients.

Contribution

It introduces Wolff potential estimates for the stationary Stokes system with Dini-BMO coefficients, extending pointwise bounds to solutions without extra regularity.

Findings

Gradient estimates via Wolff potentials for Stokes systems

Pointwise bounds for solutions with minimal coefficient regularity

Extension of potential theory methods to fluid dynamics equations

Abstract

The pointwise gradient estimate for weak solution pairs to the stationary Stokes system with Dini-BMO coefficients is established via the Havin-Maz'ya-Wolff type nonlinear potential of the nonhomogeneous term. In addition, we present a pointwise bound for the weak solutions under no extra regularity assumption on the coefficients.