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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.02562 |
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| _version_ | 1866909197341294592 |
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| author | He, Siming |
| author_facet | He, Siming |
| contents | We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small $L^1$-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi, can suppress the chemotactic blow-up in these systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02562 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part I: Alternating Flows He, Siming Analysis of PDEs We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS) subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three-dimension and has finite-time blow-up solutions with arbitrarily small $L^1$-mass. In this study, we show that a family of time-dependent alternating shear flows, inspired by the clever ideas of Tarek Elgindi, can suppress the chemotactic blow-up in these systems. |
| title | Time-dependent Flows and Their Applications in Parabolic-parabolic Patlak-Keller-Segel Systems Part I: Alternating Flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.02562 |