GLOBAL ATTRACTORS TO THREE-DIMENSIONAL NAVIER-STOKES EQUATIONS WITH DAMPING AND FINITE DELAYS

DOI: 10.18173/2354-1059.2025-0016

Tóm tắt

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 Ω ⊂ R3. 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.