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In 2007, Constantin and Ramos proved a result on the vanishing long timeaverage enstrophy dissipation rate in the inviscid limit of the 2D dampedNavier-Stokes equations. In this work, we prove a generalization of this forthe p-enstrophy, sequences of distributions of initial data and sequences ofstrongly converging right-hand sides. We simplify their approach by workingwith invariant measures on the global attractors which can be characterized viabounded complete solution trajectories. Then, working on the level oftrajectories allows us to directly employ some recent results on strongconvergence of the vorticity in the inviscid limit.

Vanishing of long time average p-enstrophy dissipation rate in the inviscid limit of the 2D damped Navier-Stokes equations