# Commutator Estimates for the Dirichlet-to-Neumann Map of Stokes Systems in Lipschitz Domains

## TL;DR

This paper develops commutator estimates for the Dirichlet-to-Neumann map associated with Stokes systems in Lipschitz domains, extending harmonic analysis techniques to fluid mechanics boundary problems.

## Contribution

It extends Dahlberg's bilinear estimates and previous work on harmonic analysis to establish new commutator estimates for Stokes systems in Lipschitz domains.

## Key findings

- Established commutator estimates for Stokes systems
- Extended harmonic analysis techniques to fluid boundary problems
- Provided a framework for further analysis of Stokes systems in irregular domains

## Abstract

In the paper, we establish commutator estimates for the Dirichlet-to-Neumann map of Stokes systems in Lipschitz domains. The approach is based on Dahlberg's bilinear estimates, and the results may be regarded as an extension of [Dahlberg, Poisson semigroups and singular integrals, Proc. Amer. Math. Soc., 97(1986), no.1, 41-48.] and [Shen, Commutator estimates for the Dirichlet-to-Neumann map in Lipschitz domains, Some topics in harmonic analysis and applications, 369C384, Adv. Lect. Math. (ALM)34, Int. Press, Somerville, MA, 2016.] to Stokes systems.