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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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