Decay characterization of solutions to the Navier-Stokes-Voigt equations in terms of the initial datum

TL;DR

This paper analyzes how solutions to the Navier-Stokes-Voigt equations decay over time based on the initial data's decay properties, providing insights into their long-term behavior and relation to linear solutions.

Contribution

It characterizes the decay rates of solutions to the Navier-Stokes-Voigt equations in relation to initial data decay, enhancing understanding of their asymptotic behavior.

Findings

Decay rates depend on initial data decay character

Solutions exhibit specific long-term decay behavior

Comparison with linear solutions reveals asymptotic properties

Abstract

The Navier-Stokes-Voigt equations are a regularization of the Navier-Stokes equations that share some of its asymptotic and statistical properties and have been used in direct numerical simulations of the latter. In this article we characterize the decay rate of solutions to the Navier-Stokes-Voigt equations in terms of the decay character of the initial datum and study the long time behaviour of its solutions by comparing them to solutions to the linear part.