Periodic solutions of the parabolic–elliptic Keller–Segel system on whole spaces

In this paper, we investigate to the existence and uniqueness of periodic solutions for the parabolic–elliptic Keller–Segel system on whole spaces detailized by Euclidean space Rn(wheren⩾4)$\mathbb {R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real hyperbolic space Hn(wheren⩾2)$\mathbb {H}^n\,\, (\hbo...

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Bibliographic Details
Published in:Mathematische Nachrichten 2024-08, Vol.297 (8), p.3003-3023
Main Authors: Loan, Nguyen Thi, Nguyen Thi, Van Anh, Van Thuy, Tran, Xuan, Pham Truong
Format: Article
Language:English
Subjects:
Asymptotic methods
dispersive estimates
Euclidean geometry
exponential stability
Hyperbolic coordinates
Keller–Segel system
Lorentz spaces
periodic solutions
polynomial stability
smoothing estimates
unconditional uniqueness
well‐posedness
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Summary:In this paper, we investigate to the existence and uniqueness of periodic solutions for the parabolic–elliptic Keller–Segel system on whole spaces detailized by Euclidean space Rn(wheren⩾4)$\mathbb {R}^n\,\,(\hbox{ where }n \geqslant 4)$ and real hyperbolic space Hn(wheren⩾2)$\mathbb {H}^n\,\, (\hbox{where }n \geqslant 2)$. We work in framework of critical spaces such as on weak‐Lorentz space Ln2,∞(Rn)$L^{\frac{n}{2},\infty }(\mathbb {R}^n)$ to obtain the results for the Keller–Segel system on Rn$\mathbb {R}^n$ and on Lp2(Hn)$L^{\frac{p}{2}}(\mathbb {H}^n)$ for n
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.202300311