- Path:
Periodical
- Title:
- Advances in nonlinear analysis
- Publication:
-
Berlin Boston, Mass.: de Gruyter
- Note:
- Gesehen am 18.03.2019
- Fortsetzung der Druck-Ausgabe
- Open Access
- Namensnennung 4.0 International
- Scope:
- Online-Ressource
- ISSN:
- 2191-950X
- ZDB-ID:
-
2645915-2
- VÖBB-Katalog:
- 15630346
- Keywords:
- Zeitschrift
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- Rights reserved
- Accessibility:
- Free Access
Article
- Title:
- Well-posedness of Cauchy problem of fractional drift diffusion system in non-critical spaces with power-law nonlinearity
- Publication:
-
Berlin Boston, Mass.: de Gruyter, 2024
- Language:
- English
- Information:
- Abstract: In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of the convention that people always focus on the properties of the solution in critical spaces, here we are interested in non-critical spaces such as supercritical Sobolev spaces and subcritical Lebesgue spaces. For the initial data in these non-critical spaces, using the properties of fractional heat semigroup and the classical Hardy-Littlewood-Sobolev inequality, we obtain the existence and uniqueness of the mild solution, together with the decaying rate estimates in terms of time variable.
- Scope:
- Online-Ressource
- Note:
- Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- drift-diffusion system ; Keller-Segel equations ; global solutions ; fractional Laplacian ; higher-order nonlinearity ; multi-linear operator ; 35K45 ; 35K55 ; 35Q60 ; 35B40
- Classification:
- Mathematik
- Collection:
- Mathematik
- Copyright:
- CC BY
- Accessibility:
- Free Access
