Well-posedness and ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces
We study the Cauchy problem for a multidimensional chemotaxis system in critical Besov spaces Ḃp,1dp−2(Rd)×(Ḃp,1dp−1(Rd))d. For 1≤p2d. More precisely, we construct a specific initial data which can be arbitrarily small in the Besov spaces. Meanwhile, the corresponding solution u can be arbitrarily...
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| Veröffentlicht in: | Nonlinear analysis 2020-07, Vol.196, p.111782, Article 111782 |
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| container_title | Nonlinear analysis |
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| creator | Nie, Yao Yuan, Jia |
| description | We study the Cauchy problem for a multidimensional chemotaxis system in critical Besov spaces Ḃp,1dp−2(Rd)×(Ḃp,1dp−1(Rd))d. For 1≤p2d. More precisely, we construct a specific initial data which can be arbitrarily small in the Besov spaces. Meanwhile, the corresponding solution u can be arbitrarily large after an arbitrarily short time. |
| doi_str_mv | 10.1016/j.na.2020.111782 |
| format | Article |
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Meanwhile, the corresponding solution u can be arbitrarily large after an arbitrarily short time.</description><identifier>ISSN: 0362-546X</identifier><identifier>EISSN: 1873-5215</identifier><identifier>DOI: 10.1016/j.na.2020.111782</identifier><language>eng</language><publisher>Elmsford: Elsevier Ltd</publisher><subject>Besov spaces ; Cauchy problems ; Chemotaxis model ; Function space ; Ill-posedness ; Norm inflation ; Well posed problems ; Well-posedness</subject><ispartof>Nonlinear analysis, 2020-07, Vol.196, p.111782, Article 111782</ispartof><rights>2020 Elsevier Ltd</rights><rights>Copyright Elsevier BV Jul 2020</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c388t-e9f272c219d1233ca6b4911794a5fcda20e821f403943d989367fc38331c30a93</citedby><cites>FETCH-LOGICAL-c388t-e9f272c219d1233ca6b4911794a5fcda20e821f403943d989367fc38331c30a93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.na.2020.111782$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3550,27924,27925,45995</link.rule.ids></links><search><creatorcontrib>Nie, Yao</creatorcontrib><creatorcontrib>Yuan, Jia</creatorcontrib><title>Well-posedness and ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces</title><title>Nonlinear analysis</title><description>We study the Cauchy problem for a multidimensional chemotaxis system in critical Besov spaces Ḃp,1dp−2(Rd)×(Ḃp,1dp−1(Rd))d. 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| source | Elsevier ScienceDirect Journals Complete |
| subjects | Besov spaces Cauchy problems Chemotaxis model Function space Ill-posedness Norm inflation Well posed problems Well-posedness |
| title | Well-posedness and ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces |
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