Suppression of blow-up in 3-D Keller-Segel system with fractional diffusion via Couette flow in whole space
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915404137365504 |
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| author | Deng, Shijin Shi, Binbin Wang, Weike Wang, Yucheng |
| author_facet | Deng, Shijin Shi, Binbin Wang, Weike Wang, Yucheng |
| contents | In this paper, we consider a Keller-Segel model with a fractional diffusion term in $\mathbb{R}^3$ in the background of a Couette flow. We show that when the background Couette flow is large enough, the dissipation enhancement induced could prevent the blow-up of solutions and thus prove the global existence and also obtain time decay rates of the solution in $L^p$ norm. The main tool of the proof is a corresponding Green's function and the key estimate is its $L^1$ estimate without singularities at $t=0$. To fulfill such an estimate, we meet great troubles caused by the fractional heat kernel together with the Couette flow in the model considered here and overcome the troubles by introducing a space-frequency mixed decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16160 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Suppression of blow-up in 3-D Keller-Segel system with fractional diffusion via Couette flow in whole space Deng, Shijin Shi, Binbin Wang, Weike Wang, Yucheng Analysis of PDEs In this paper, we consider a Keller-Segel model with a fractional diffusion term in $\mathbb{R}^3$ in the background of a Couette flow. We show that when the background Couette flow is large enough, the dissipation enhancement induced could prevent the blow-up of solutions and thus prove the global existence and also obtain time decay rates of the solution in $L^p$ norm. The main tool of the proof is a corresponding Green's function and the key estimate is its $L^1$ estimate without singularities at $t=0$. To fulfill such an estimate, we meet great troubles caused by the fractional heat kernel together with the Couette flow in the model considered here and overcome the troubles by introducing a space-frequency mixed decomposition. |
| title | Suppression of blow-up in 3-D Keller-Segel system with fractional diffusion via Couette flow in whole space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.16160 |