Abstract
We consider the damped and driven Navier–Stokes system with stress free boundary conditions and the damped Euler system in a bounded domain Ω⊂R2. We show that the damped Euler system has a (strong) global attractor in H1(Ω). 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 H1(Ω) to the strong global attractor of the limiting damped Euler system (whose solutions are not necessarily unique).
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