Enhanced dissipation and blow-up suppression for an aggregation equation with fractional diffusion and shear flow
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909180106899456 |
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| author | Binqian, Niu Shi, Binbin Wang, Weike |
| author_facet | Binqian, Niu Shi, Binbin Wang, Weike |
| contents | In this paper, we consider an aggregation equation with fractional diffusion and large shear flow, which arise from modelling chemotaxis in bacteria. Without the advection, the solution of aggregation equation may blow up in finite time. First, we study the enhanced dissipation of shear flow by resolvent estimate method, where the fractional Laplacian $(-Δ)^{α/2}$ is considered and $α\in (0,2)$. Next, we show that the enhanced dissipation of shear flow can suppress blow-up of solution to aggregation equation with fractional diffusion and establish global classical solution in the case of $α\geq 3/2$. Here we develop some new technical to overcome the difficult of low regularity for fractional Laplacian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2404_15674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enhanced dissipation and blow-up suppression for an aggregation equation with fractional diffusion and shear flow Binqian, Niu Shi, Binbin Wang, Weike Analysis of PDEs 35A01, 35Q92, 35R11, 76F10 In this paper, we consider an aggregation equation with fractional diffusion and large shear flow, which arise from modelling chemotaxis in bacteria. Without the advection, the solution of aggregation equation may blow up in finite time. First, we study the enhanced dissipation of shear flow by resolvent estimate method, where the fractional Laplacian $(-Δ)^{α/2}$ is considered and $α\in (0,2)$. Next, we show that the enhanced dissipation of shear flow can suppress blow-up of solution to aggregation equation with fractional diffusion and establish global classical solution in the case of $α\geq 3/2$. Here we develop some new technical to overcome the difficult of low regularity for fractional Laplacian. |
| title | Enhanced dissipation and blow-up suppression for an aggregation equation with fractional diffusion and shear flow |
| topic | Analysis of PDEs 35A01, 35Q92, 35R11, 76F10 |
| url | https://arxiv.org/abs/2404.15674 |