Inviscid limit for Navier-Stokes equations in domains with permeable boundaries

TL;DR

This paper investigates the inviscid limit of 2D Navier-Stokes equations with permeable boundaries, demonstrating convergence to Euler solutions satisfying Navier boundary conditions on inflow zones.

Contribution

It establishes the inviscid limit for Navier-Stokes in multiply-connected domains with permeable walls under Navier boundary conditions.

Findings

Inviscid limit proven for permeable boundary conditions

Euler solutions satisfy Navier boundary conditions on inflow zones

Results extend understanding of fluid behavior in complex domains

Abstract

This work is concerned with 2D-Navier Stokes equations in a multiply-connected bounded domain with permeable walls. The permeability is described by a Navier type condition. Our aim is to show that the inviscid limit is a solution of the Euler equations, satisfying the Navier type condition on the inflow zone of the walls.