Asymptotic behavior of solutions to 3D incompressible Navier-Stokes equations with damping

TL;DR

This paper investigates how solutions to 3D incompressible Navier-Stokes equations with damping decay over time, providing bounds on their asymptotic behavior in three-dimensional space.

Contribution

It establishes upper bounds on the decay rates of solutions to damped Navier-Stokes equations in three dimensions, extending understanding of long-term solution behavior.

Findings

Derived upper bounds for decay rates of solutions

Extended decay analysis to generalized Navier-Stokes equations with damping

Provided insights into asymptotic stability of solutions

Abstract

In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.