Uniform Dynamical Stability of Pullback Attractors for Lagrangian‐Averaged Navier–Stokes Equations With Delays

ABSTRACT The paper is devoted to the dynamical stability of pullback attractors for non‐autonomous Lagrangian‐averaged Navier–Stokes equations with delays. First, using the Ascoli–Arzelà theorem, we prove the pullback asymptotic compactness of solution operators to establish the existence of pullback attractors. Second, we prove the pointwise upper semicontinuity of pullback attractors as the delay time approaches zero. Eventually, we further investigate their uniform upper semicontinuity when the delay time converges to zero. Combining these two results, the latter strengthens the former. To the best of our knowledge, this paper appears to be the first to address both types of upper semicontinuity for pullback attractors, particularly the interesting uniform case.