Singular limit problem for the Keller–Segel system and drift-diffusion system in scaling critical Besov–Morrey spaces

A singular limit problem for the Cauchy problem of the Keller–Segel equation is considered in a critical function space based on Morrey spaces. A solution to the Keller–Segel system in a scaling critical function space converges to a solution to the drift-diffusion system of parabolic-elliptic type...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-01, Vol.529 (2), p.127207, Article 127207
Main Authors: Nogayama, Toru, Sawano, Yoshihiro
Format: Article
Language:English
Subjects:
Drift-diffusion system
Global well-posedness
Keller–Segel equation
Lorentz spaces
Scaling invariance
Singular limit problem
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Summary:A singular limit problem for the Cauchy problem of the Keller–Segel equation is considered in a critical function space based on Morrey spaces. A solution to the Keller–Segel system in a scaling critical function space converges to a solution to the drift-diffusion system of parabolic-elliptic type in the critical space strongly as the relaxation time tends to infinity. The key ingredient is a Banach space-valued Lorentz space in time. By the careful use of the real interpolation, a sharp estimate for the heat semigroup is obtained.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127207