Asymptotic study of Leray Solution of 3D-NSE With Exponential Damping

TL;DR

This paper investigates the long-term behavior, uniqueness, and stability of Leray solutions to the 3D Navier-Stokes equations incorporating a nonlinear exponential damping term, extending previous work on solution properties.

Contribution

It provides a detailed asymptotic analysis of Leray solutions with exponential damping, focusing on their uniqueness, continuity in $L^2$, and decay properties over time.

Findings

Proved uniqueness of solutions under exponential damping

Established continuity in $L^2$ norm over time

Demonstrated decay of solutions as time approaches infinity

Abstract

We study the uniqueness, the continuity in $L^2$ and the large time decay for the Leray solutions of the $3D$ incompressible Navier-Stokes equations with the nonlinear exponential damping term $a (e^{b |u|^{\bf 2}}-1)u$, ($a,b>0$) studied by the second author in \cite{J1}.