Large time behavior of solutions to a diffusion approximation radiation hydrodynamics model

TL;DR

This paper studies the long-term behavior of solutions to a radiation hydrodynamics model, establishing global existence, decay rates, and extending results to related systems, using advanced mathematical techniques.

Contribution

It provides the first comprehensive analysis of large time behavior for this model, including decay rates and well-posedness in Sobolev spaces with Littlewood-Paley techniques.

Findings

Global-in-time well-posedness in Sobolev spaces

Optimal decay rates under additional conditions

Extension of results to related diffusion systems without thermal conductivity

Abstract

This paper concerns with the large time behavior of solutions to a diffusion approximation radiation hydrodynamics model when the initial data is a small perturbation around an equilibrium state. The global-in-time well-posedness of solutions is achieved in Sobolev spaces depending on the Littlewood-Paley decomposition technique together with certain elaborate energy estimates in frequency space. Moreover, the optimal decay rate of the solution is also yielded provided the initial data also satisfy an additional $L^1$ condition. Meanwhile, the similar results of the diffusion approximation system without the thermal conductivity could be also established.