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Inviscid limit for damped and driven incompressible Navier-Stokes equations in \(\mathbb R^2\). (English) Zbl 1151.35068

In this paper the zero viscosity limit of long time averages of solutions to damped and driven Navier-Stokes equations in \(\mathbb R^{2}\) is considered. The authors prove that the rate of dissipation of enstrophy vanishes. It can be shown that stationary statistical solutions of the damped and driven Navier-Stokes equations converge to renormalized stationary statistical solutions of the damped and driven Euler equations. These solutions obey the enstrophy balance.

MSC:

35Q30 Navier-Stokes equations
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
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