Optimal time-decay for Euler-Fourier system with damping in the critical L² framework

2025/05/08 by Liu, Jing, Gu, Lianchao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.05187

Abstract

This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in ℝ^d~(d≥1). A time-weighted energy argument has been developed within the L² framework to derive the optimal time-decay rates, which enables us to remove the smallness of low-frequencies of initial data. A great part of our analysis relies on the study of a Lyapunov functional in the spirit of [13], which mainly depends on some elaborate use of non-classical Besov product estimates and interpolations. Exhibiting a damped mode with faster time decay than the whole solution also plays a key role.

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