Pullback attractors of 2D Navier–Stokes equations with weak damping, distributed delay, and continuous delay

Abstract

In this present paper, the existence of pullback attractors for the 2D Navier-Stokes equation with weak damping, distributed delay, and continuous delay has been considered, by virtue of classical Galerkin's method, we derived the existence and uniqueness of global weak and strong solutions. Using the Aubin-Lions lemma and some energy estimate in the Banach space with delay, we obtained the uniform bounded and existence of uniform pullback absorbing ball for the solution semi-processes; we concluded the pullback attractors via verifying the pullback asymptotical compactness by the generalized Arzelà-Ascoli theorem.

Double stabilities of pullback random attractors for stochastic delayed p‐Laplacian equations

“…2,5,6,[22][23][24][25][26] It is worth pointing out that there is no paper studying the stochastic delayed p-Laplacian equation, although other delayed equations had been well investigated. 16,17,[27][28][29][30][31][32] For Equation (3) even for the simpler cases such as deterministic equation (b j = 0) or bounded domain, it has not been solved for the existence (let alone backward compactness) of a pullback attractor in X = C([− , 0], X), where X = L 2 (R n ).…”