Abstract
We study the first initial boundary value problem for the non-autonomous 2D g-Navier–Stokes equations in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality. We show the existence and some further results of a pullback attractor for the process generated by strong solutions to the problem with respect to a large class of non-autonomous forcing terms. To overcome the difficulty caused by the unboundedness of the domain, the proof is based on a pullback asymptotic compactness argument and the use of the enstrophy equation.
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Quyet, D.T., Thuy, L.T. Pullback Attractors in \(V_g\) for Non-autonomous 2D g-Navier–Stokes Equations in Unbounded Domains. Differ Equ Dyn Syst 32, 293–312 (2024). https://doi.org/10.1007/s12591-021-00571-x
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DOI: https://doi.org/10.1007/s12591-021-00571-x