## Vanishing viscosity limit for global attractors for the damped Navier-Stokes system with stress free boundary conditions.(English)Zbl 1398.35145

Summary: We consider the damped and driven Navier-Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain $$\Omega \subset \mathbb{R}^2$$. 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 strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).

### MSC:

 35Q30 Navier-Stokes equations 35B41 Attractors 76D05 Navier-Stokes equations for incompressible viscous fluids 37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
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### References:

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