On the existence of global solutions for the 3D chemorepulsion system
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913387107057664 |
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| author | Cieślak, Tomasz Fuest, Mario Hajduk, Karol Sierżęga, Mikołaj |
| author_facet | Cieślak, Tomasz Fuest, Mario Hajduk, Karol Sierżęga, Mikołaj |
| contents | In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that $\nabla\sqrt{u} \in L^4(0, T; L^2(Ω))$. Our method is related to the Bakry--Émery calculation and appears to be new in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_09620 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the existence of global solutions for the 3D chemorepulsion system Cieślak, Tomasz Fuest, Mario Hajduk, Karol Sierżęga, Mikołaj Analysis of PDEs 35B45, 35K45 (primary), 92C17 (secondary) In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that $\nabla\sqrt{u} \in L^4(0, T; L^2(Ω))$. Our method is related to the Bakry--Émery calculation and appears to be new in this context. |
| title | On the existence of global solutions for the 3D chemorepulsion system |
| topic | Analysis of PDEs 35B45, 35K45 (primary), 92C17 (secondary) |
| url | https://arxiv.org/abs/2303.09620 |