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arXiv · 1706.00607

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

Vladimir Chepyzhov·Alexei Ilyin·Sergey Zelik
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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).

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Vladimir Chepyzhov, Alexei Ilyin, Sergey Zelik. 2017-06-02. Vanishing viscosity limit for global attractors for the damped Navier--Stokes system with stress free boundary conditions. https://doi.org/10.1016/j.physd.2017.08.005

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