Well-posedness and ill-posedness of a multidimensional chemotaxis system in the critical Besov spaces

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
Hauptverfasser: Nie, Yao, Yuan, Jia
Format: Artikel
Sprache:eng
Schlagworte:
Besov spaces
Cauchy problems
Chemotaxis model
Function space
Ill-posedness
Norm inflation
Well posed problems
Well-posedness
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Zusammenfassung: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2020.111782