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arXiv · 2508.01369

Cauchy problems for time-space fractional coupled chemotaxis-fluid equations in Besov-Morrey spaces

Yong Zhen Yang·Yong Zhou·Xiao Lin Liu
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Abstract

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.

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Yong Zhen Yang, Yong Zhou, Xiao Lin Liu. 2025-08-02. Cauchy problems for time-space fractional coupled chemotaxis-fluid equations in Besov-Morrey spaces. https://arxiv.org/abs/2508.01369

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