Long Time Decay of Leray Solution of 3D-NSE With Exponential Damping

TL;DR

This paper investigates the long-term behavior, uniqueness, and decay properties of Leray solutions to the 3D Navier-Stokes equations incorporating a nonlinear exponential damping term, providing insights into their stability and decay over time.

Contribution

It introduces and analyzes the effects of a nonlinear exponential damping term on Leray solutions of the 3D Navier-Stokes equations, focusing on decay and uniqueness properties.

Findings

Establishes decay rates for solutions with exponential damping

Proves uniqueness and continuity in L^2 for the modified equations

Demonstrates large time decay behavior of Leray solutions

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 nonlinear exponential damping term $a (e^{b |u|^{\bf 4}}-1)u$, ($a,b>0$).