Parabolic-elliptic Keller-Segel's system
Tunisian J. Math. 6 (2024) 503-542 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...
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| creator | Lemarié, Valentin |
| description | Tunisian J. Math. 6 (2024) 503-542 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. |
| doi_str_mv | 10.48550/arxiv.2307.05981 |
| format | Article |
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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.</description><identifier>DOI: 10.48550/arxiv.2307.05981</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2023-07</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2307.05981$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.2140/tunis.2024.6.503$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.48550/arXiv.2307.05981$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lemarié, Valentin</creatorcontrib><title>Parabolic-elliptic Keller-Segel's system</title><description>Tunisian J. Math. 6 (2024) 503-542 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.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzj2LAjEUheE0FsvoD9jK6bTJmJtMkplSRF1ZYQXth3zcSCCiZET037vrWp23OjyEfAKr6kZKNjP5Hm8VF0xXTLYNfJDpzmRjzyk6iinFyzW68vu3MNM9HjFN-rJ_9Fc8DckgmNTj6L0FOayWh8UX3f6sN4v5lhqlgQbhrWXgnQ9NbesWlA1eIWj0KhgugDupUbXKCs6c92hBSoGKawumZl4UZPx_-6J2lxxPJj-6P3L3IosnGjI7nQ</recordid><startdate>20230712</startdate><enddate>20230712</enddate><creator>Lemarié, Valentin</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230712</creationdate><title>Parabolic-elliptic Keller-Segel's system</title><author>Lemarié, Valentin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a671-f3dbb01dcdf84b4916bfd6e17ed6fa2312c57e696b320cddeb1553e627b1a40d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Lemarié, Valentin</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lemarié, Valentin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Parabolic-elliptic Keller-Segel's system</atitle><date>2023-07-12</date><risdate>2023</risdate><abstract>Tunisian J. Math. 6 (2024) 503-542 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.</abstract><doi>10.48550/arxiv.2307.05981</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Analysis of PDEs |
| title | Parabolic-elliptic Keller-Segel's system |
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