# Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity

## TL;DR

This paper introduces a 3D Navier-Stokes-Voigt fluid model with a memory term replacing instantaneous viscosity, demonstrating the existence of a finite-dimensional exponential attractor despite weaker dissipation.

## Contribution

It establishes the existence of a regular exponential attractor for a Navier-Stokes-Voigt model with memory, under sharp conditions, extending understanding of hereditary fluid effects.

## Key findings

- Existence of a finite fractal dimension exponential attractor.
- Weaker dissipation compared to models with both hereditary and instantaneous viscosity.
- Conditions on the memory kernel for attractor existence.

## Abstract

We consider a Navier-Stokes-Voigt fluid model where the instantaneous kinematic viscosity has been completely replaced by a memory term incorporating hereditary effects, in presence of Ekman damping. The dissipative character of our model is weaker than the one where hereditary and instantaneous viscosity coexist, previously studied by Gal and Tachim-Medjo. Nevertheless, we prove the existence of a regular exponential attractor of finite fractal dimension under rather sharp assumptions on the memory kernel.