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

Abstract

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.

References in corpus (1)

• Energy and enstrophy dissipation in steady state 2-d turbulence

Cited by in corpus (1)

• Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit