# Behaviour of the Stokes operators under domain perturbation

## TL;DR

This paper investigates how the resolvents of different Stokes operators, defined on varying domains with Dirichlet boundary conditions, behave and converge as the domain geometry changes.

## Contribution

It provides a detailed analysis of the convergence of resolvents of multiple Stokes operators under domain perturbations.

## Key findings

- Resolvents of Stokes operators converge with domain changes.
- Different definitions of Stokes operators are considered.
- Results depend on the domain geometry and boundary conditions.

## Abstract

Depending of the geometry of the domain, one can define --at least-- three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains.