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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2505.05187 |
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| _version_ | 1866913826657533952 |
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| author | Liu, Jing Gu, Lianchao |
| author_facet | Liu, Jing Gu, Lianchao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal time-decay for Euler-Fourier system with damping in the critical $L^2$ framework Liu, Jing Gu, Lianchao Analysis of PDEs 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. |
| title | Optimal time-decay for Euler-Fourier system with damping in the critical $L^2$ framework |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.05187 |