Cauchy problems for time-space fractional coupled chemotaxis-fluid equations in Besov-Morrey spaces
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909718914531328 |
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| author | Yang, Yong Zhen Zhou, Yong Liu, Xiao Lin |
| author_facet | Yang, Yong Zhen Zhou, Yong Liu, Xiao Lin |
| contents | In this paper, we consider the Cauchy problems for the time-space fractional coupled chemotaxis-fluid equations, which is a generalized form of the coupled chemotaxis-fluid equations studied in \cite{M.H. Yang}. In contrast to \cite{M.H. Yang}, the solution operator of the system does not satisfy the semigroup effect, which makes the approach of \cite{M.H. Yang} inapplicable. Based on the theory of harmonic analysis, using techniques such as real interpolation, embedding in Besov-Morrey spaces, the multiplier theorem, and the Hardy-Littelwood inequality in Morrey spaces, we establish global existence. As an application, we analysis the asymptotic behavior of the solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01369 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cauchy problems for time-space fractional coupled chemotaxis-fluid equations in Besov-Morrey spaces Yang, Yong Zhen Zhou, Yong Liu, Xiao Lin Analysis of PDEs In this paper, we consider the Cauchy problems for the time-space fractional coupled chemotaxis-fluid equations, which is a generalized form of the coupled chemotaxis-fluid equations studied in \cite{M.H. Yang}. In contrast to \cite{M.H. Yang}, the solution operator of the system does not satisfy the semigroup effect, which makes the approach of \cite{M.H. Yang} inapplicable. Based on the theory of harmonic analysis, using techniques such as real interpolation, embedding in Besov-Morrey spaces, the multiplier theorem, and the Hardy-Littelwood inequality in Morrey spaces, we establish global existence. As an application, we analysis the asymptotic behavior of the solutions. |
| title | Cauchy problems for time-space fractional coupled chemotaxis-fluid equations in Besov-Morrey spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.01369 |