Vanishing of Long Time average p-enstrophy Dissipation Rate in the Inviscid Limit of the 2D Damped Navier–Stokes Equations

Abstract

In Constantin and Ramos (Commun Math Phys 275(2), 529–551, 2007), Constantin and Ramos proved a result on the vanishing long time average enstrophy dissipation rate in the inviscid limit of the 2D damped Navier–Stokes equations. In this work, we prove a generalization of this for the p-enstrophy, 1<p<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1< p < \\infty $$\\end{document}, sequences of distributions of initial data and sequences of strongly converging right-hand sides. We simplify their approach by working with invariant measures on the global attractors which can be characterized via bounded complete solution trajectories. Then, working on the level of trajectories allows us to directly employ some recent results on strong convergence of the vorticity in the inviscid limit.