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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2402.16536 |
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| _version_ | 1866929256735440896 |
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| author | Tu, Bowei |
| author_facet | Tu, Bowei |
| contents | We consider the Cauchy problem of the three-dimensional parabolic-elliptic Patlak-Keller-Segel chemotactic model. The initial data is almost a Dirac measure supported on a straight line with mass less than $8π$. We prove that if the data is sufficiently close to the straight line, then global well-posedness holds. This result is parallel to the work on vortex filament solutions of the Navier-Stokes equations by Bedrossian, Germain and Harrop-Griffiths \cite{filament}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16536 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of the 3D Patlak-Keller-Segel system near a straight line Tu, Bowei Analysis of PDEs We consider the Cauchy problem of the three-dimensional parabolic-elliptic Patlak-Keller-Segel chemotactic model. The initial data is almost a Dirac measure supported on a straight line with mass less than $8π$. We prove that if the data is sufficiently close to the straight line, then global well-posedness holds. This result is parallel to the work on vortex filament solutions of the Navier-Stokes equations by Bedrossian, Germain and Harrop-Griffiths \cite{filament}. |
| title | Global well-posedness of the 3D Patlak-Keller-Segel system near a straight line |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.16536 |