Global existence and decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics

TL;DR

This paper establishes the global existence and optimal decay rates of strong solutions to a radiation hydrodynamics model combining Navier-Stokes and radiative diffusion equations, assuming small initial perturbations.

Contribution

It proves global well-posedness and decay rates for the model using frequency decomposition and Fourier analysis, advancing understanding of radiation-fluid interactions.

Findings

Global strong solutions exist under small initial perturbations.

Optimal decay rates including highest-order derivatives are derived.

Methodology combines frequency decomposition and energy techniques.

Abstract

In this paper, we study the global well-posedness and optimal time decay rates of strong solutions to the diffusion approximation model in radiation hydrodynamics in $\mathbb{R}^3$. This model consists of the full compressible Navier-Stokes equations and the radiative diffusion equation which describes the influence and interaction between thermal radiation and fluid motion. Supposing that the initial perturbation around the equilibrium is sufficiently small in $H^2$-norm, we obtain the global strong solutions by utilizing method of the frequency decomposition. Moreover, by performing Fourier analysis techniques and using the delicate energy method, we consequently derive the optimal decay rates (including highest-order derivatives) of solutions for this model.