Higher-order boundary layers and regularity for Stokes systems over rough boundaries

TL;DR

This paper develops higher-order boundary layer correctors for the Stokes system in rough, oscillating domains, leading to advanced regularity estimates and Liouville theorems, with implications for fluid dynamics over complex boundaries.

Contribution

It introduces a general method for constructing boundary layer correctors of arbitrary order for the Stokes system in rough domains, extending previous first and second order results.

Findings

Established large-scale boundary regularity estimates.

Proved a Liouville theorem of arbitrary order.

Connected results to higher-order boundary layer tails and wall laws.

Abstract

In this paper, we study the large-scale boundary regularity for the Stokes system in periodically oscillating John domains. Our main contribution is the construction of boundary layer correctors of arbitrary order. This is a significant generalization of the known results restricted to the first and second orders. As an application, we prove the large-scale regularity estimate, as well as a Liouville theorem, of arbitrary order for the Stokes system. Our results are also related to higher-order boundary layer tails and wall laws in viscous fluids over rough boundaries.