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

P. Constantin; F. Ramos

doi:10.1007/s00220-007-0310-7

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

P. Constantin·F. Ramos

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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.

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P. Constantin, F. Ramos. 2006-11-27. Inviscid limit for damped and driven incompressible Navier-Stokes equations in ${{\mathbb R}^2}$. https://doi.org/10.1007/s00220-007-0310-7

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