Large time asymptotic behavior of the compressible Navier-Stokes Equations in partial Space-Periodic Domains

TL;DR

This paper investigates the long-term behavior of 3D compressible Navier-Stokes equations in partial space-periodic domains, revealing reduced profile systems akin to lower-dimensional Navier-Stokes equations with modified pressure functions.

Contribution

It introduces a novel analysis of large time asymptotics for compressible Navier-Stokes in partial periodic domains, linking profile systems to lower-dimensional equations.

Findings

Profile systems resemble lower-dimensional Navier-Stokes equations

Large time behavior characterized in partial space-periodic domains

Energy methods and linearized analysis underpin results

Abstract

In this paper, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable "pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.