# Longtime behavior for 3D Navier-Stokes equations with constant delays

## TL;DR

This paper studies the long-term dynamics of delayed 3D Navier-Stokes equations, establishing the existence and nature of attractors under large viscosity assumptions.

## Contribution

It introduces a novel analysis of attractors for delayed 3D Navier-Stokes equations, linking linearized and original systems to demonstrate attractor properties.

## Key findings

- Existence of a unique local attractor for large viscosity
- Attractor reduces to a singleton set
- Analysis based on linearized system dynamics

## Abstract

This paper investigates the longtime behavior of delayed 3D Navier-Stokes equations in terms of attractors. The study will strongly rely on the investigation of the linearized Navier-Stokes system, and the relationship between the discrete dynamical flow for the linearized system and the continuous flow associated to the original system. Assuming the viscosity to be sufficiently large, there exists a unique local attractor for the delayed 3D Navier-Stokes equations. Moreover, the local attractor reduces to a singleton set.