Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$

Details Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$ Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$

2006-11-27

arxiv.org/abs/math/0611782v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00220-007-0310-7

We consider the zero viscosity limit of long time averages of solutions of damped and driven Navier-Stokes equations in ${\mathbb R}^2$. We prove that the rate of dissipation of enstrophy vanishes. 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.

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