Stability analysis of time-periodic solutions to the Navier-Stokes-Fourier system in 3D whole space

TL;DR

This paper investigates the stability and decay behavior of perturbations around time-periodic solutions to the 3D Navier-Stokes-Fourier system, providing decay estimates under small initial perturbations.

Contribution

It establishes the large-time decay estimates for perturbations around time-periodic solutions in 3D, utilizing Besov space techniques and linearized semigroup analysis.

Findings

Decay estimates for perturbations established

Stability of time-periodic solutions demonstrated

Effective use of Besov space estimates in proof

Abstract

This paper concerns the large-time behavior of perturbations around a time-periodic solution to the Navier-Stokes-Fourier system in the three-dimensional whole space. The time-periodic solution exists when a given external force is small enough. We derive the time-decay estimate of the perturbation under the assumption that an initial perturbation is sufficiently small. The time-space integral estimate for the linearized semigroup around the constant state in the Besov spaces is effectively applied in the proof.