GLOBAL ATTRACTORS TO THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH DAMPING AND FINITE DELAYS
DOI:
https://doi.org/10.18173/2354-1059.2025-0016Keywords:
Navier-Stokes equation, global attractors, delays, dampingAbstract
The asymptotic behavior of solutions to the three-dimensional NavierStokes equations is a longstanding and challenging open problem, which has seen numerous important contributions in recent years. In this paper, we consider the NavierStokes equations with damping and delay terms on a bounded domain \( \Omega \subset \mathbb{R}^3 \). Using the energy method, we prove the existence of global attractors, thus establishing the long-time stability and compactness of the solution set for this class of delayed fluid dynamic models.
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