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arXiv · 2505.05187

Optimal time-decay for Euler-Fourier system with damping in the critical $L^2$ framework

Jing Liu·Lianchao Gu
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Abstract

This paper is concerned with the large time behavior of solutions to the Euler-Fourier system with damping in $\mathbb{R}^{d}~(d\geq1)$. A time-weighted energy argument has been developed within the $L^2$ 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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Jing Liu, Lianchao Gu. 2025-05-08. Optimal time-decay for Euler-Fourier system with damping in the critical $L^2$ framework. https://arxiv.org/abs/2505.05187

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