Parabolic-elliptic Keller-Segel's system
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909331547488256 |
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| author | Lemarié, Valentin |
| author_facet | Lemarié, Valentin |
| contents | We study on the whole space R d the compressible Euler system with damping coupled to the Poisson equation when the damping coefficient tends towards infinity. We first prove a result of global existence for the Euler-Poisson system in the case where the damping is large enough, then, in a second step, we rigorously justify the passage to the limit to the parabolic-elliptic Keller-Segel after performing a diffusive rescaling, and get an explicit convergence rate. The overall study is carried out in 'critical' Besov spaces, in the spirit of the recent survey [16] by R. Danchin devoted to partially dissipative systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_05981 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Parabolic-elliptic Keller-Segel's system Lemarié, Valentin Analysis of PDEs We study on the whole space R d the compressible Euler system with damping coupled to the Poisson equation when the damping coefficient tends towards infinity. We first prove a result of global existence for the Euler-Poisson system in the case where the damping is large enough, then, in a second step, we rigorously justify the passage to the limit to the parabolic-elliptic Keller-Segel after performing a diffusive rescaling, and get an explicit convergence rate. The overall study is carried out in 'critical' Besov spaces, in the spirit of the recent survey [16] by R. Danchin devoted to partially dissipative systems. |
| title | Parabolic-elliptic Keller-Segel's system |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2307.05981 |