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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.13992 |
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| _version_ | 1866910576245997568 |
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| author | Carrillo, José Antonio Lin, Ke |
| author_facet | Carrillo, José Antonio Lin, Ke |
| contents | The qualitative study of solutions to the coupled parabolic-elliptic chemotaxis system with nonlinear diffusion for two species will be considered in the whole Euclidean space $\mathbb{R}^d$ ($d\geq 3$). It was proven in \cite{CK2021-ANA} that there exist two critical curves that separate the global existence and blow-up of weak solutions to the above problem. We improve this result by providing sharp criteria for the dicothomy: global existence of weak solution versus blow-up below and at these curves. Besides, there exist sharp critical masses of initial data at the intersection of the two critical lines, which extend the well-known critical mass phenomenon in one-species Keller-Segel system in \cite{BCL09-CVPDE} to two-species case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13992 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sharp critical mass criteria for weak solutions to a degenerate cross-attraction system Carrillo, José Antonio Lin, Ke Analysis of PDEs The qualitative study of solutions to the coupled parabolic-elliptic chemotaxis system with nonlinear diffusion for two species will be considered in the whole Euclidean space $\mathbb{R}^d$ ($d\geq 3$). It was proven in \cite{CK2021-ANA} that there exist two critical curves that separate the global existence and blow-up of weak solutions to the above problem. We improve this result by providing sharp criteria for the dicothomy: global existence of weak solution versus blow-up below and at these curves. Besides, there exist sharp critical masses of initial data at the intersection of the two critical lines, which extend the well-known critical mass phenomenon in one-species Keller-Segel system in \cite{BCL09-CVPDE} to two-species case. |
| title | Sharp critical mass criteria for weak solutions to a degenerate cross-attraction system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.13992 |