A nonlocal Stokes system with volume constraints

TL;DR

This paper introduces a nonlocal model for the steady Stokes system with volume constraints to enforce no-slip boundary conditions, proving well-posedness and convergence to the classical solution as nonlocality diminishes.

Contribution

It presents a novel nonlocal formulation for the Stokes system with volume constraints, establishing well-posedness and convergence results.

Findings

The nonlocal model is well-posed.

Solutions converge to classical Stokes solutions as nonlocality vanishes.

The volume constraint effectively enforces no-slip boundary conditions.

Abstract

In this paper, we introduce a nonlocal model for linear steady Stokes system with physical no-slip boundary condition. We use the idea of volume constraint to enforce the no-slip boundary condition and prove that the nonlocal model is well-posed. We also show that and the solution of the nonlocal system converges to the solution of the original Stokes system as the nonlocality vanishes.