# Optimal time-decay estimates for the compressible Navier-Stokes-Poisson equations without additional smallness assumptions

## TL;DR

This paper establishes optimal time-decay estimates for solutions to the compressible Navier-Stokes-Poisson equations without requiring small initial data, using energy methods instead of spectral analysis.

## Contribution

It introduces a new decay framework for critical Besov space norms and removes the smallness assumption on low-frequency initial data.

## Key findings

- Proves large-time decay rates for global strong solutions
- Develops a decay framework based on energy methods
- Removes the smallness condition on initial data in decay analysis

## Abstract

The present paper is dedicated to the large time asymptotic behavior of global strong solutions near constant equilibrium (away from vacuum) to the compressible Navier-Stokes-Poisson equations. Precisely, we present that under the same regularity assumptions as in \cite{SX2}, a \textit{different} time-decay framework of the $\dot{B}_{p,1}^{s}$ norm of the critical global solutions is established. The proof mainly depends on the pure energy argument \textit{without the spectral analysis}, which allows us to remove \textit{the usual smallness assumption of low frequencies of initial data}.