Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913231627354112 |
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| author | Bai, Xiang Tan, Changhui Xue, Liutang |
| author_facet | Bai, Xiang Tan, Changhui Xue, Liutang |
| contents | We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter $α\in(0,1)$. This highlights the distinct feature of the alignment operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07686 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure Bai, Xiang Tan, Changhui Xue, Liutang Analysis of PDEs 35Q31, 35R11, 76N10, 35B40 We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter $α\in(0,1)$. This highlights the distinct feature of the alignment operator. |
| title | Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure |
| topic | Analysis of PDEs 35Q31, 35R11, 76N10, 35B40 |
| url | https://arxiv.org/abs/2402.07686 |