Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions

Abstract

We consider the damped and driven Navier--Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $\Omega \subset {\mathbf{R}}^2$. We show that the damped Euler system has a (strong) global attractor in~$H^1(\Omega )$. We also show that in the vanishing viscosity limit the global attractors of the Navier--Stokes system converge in the non-symmetric Hausdorff distance in $H^1(\Omega )$ to the the strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).

21 pages

References in corpus (3)

• Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${\mathbb{R}}^2$
• Infinite Energy Solutions for Damped Navier-Stokes Equations in R2
• Infinite energy solutions for Dissipative Euler equations in R^2

Cited by in corpus (1)

• Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations