一类双种群趋化–非牛顿流体耦合模型的强解
Strong Solutions for a Class of Coupled Two-Species Chemotaxis-Non-Newtonian Fluid Models
DOI: 10.12677/pm.2026.164106, PDF,    科研立项经费支持
作者: 孙 畅, 王长佳*：长春理工大学数学与统计学院，吉林 长春
关键词: 趋化–流体模型；非牛顿流；强解；存在唯一性；The Coupled Chemotaxis-Fluid Equations； Non-Newtonian Fluids； Strong Solutions； Existence and Uniqueness
摘要: 本文主要在三维光滑有界区域中对一类双种群趋化–非牛顿流体耦合模型进行研究，在适当的函数设定下，利用不动点定理，对于小且适当正则的数据，确立其强解的存在性与唯一性。
Abstract: This paper mainly investigates a class of coupled two-species chemotaxis-Non-Newtonian fluid models in a 3D smooth bounded domain. Using a fixed-point argument within an appropriate functional framework, we establish the existence and uniqueness of strong solutions for this problem, provided that the given data are sufficiently small and regular.
文章引用：孙畅, 王长佳. 一类双种群趋化–非牛顿流体耦合模型的强解[J]. 理论数学, 2026, 16(4): 213-226. https://doi.org/10.12677/pm.2026.164106

参考文献

[1] Höfer, T., Sherratt, J.A. and Maini, P.K. (1995) Cellular Pattern Formation during Dictyostelium Aggregation. Physica D: Nonlinear Phenomena, 85, 425-444. [Google Scholar] [CrossRef] 
[2] Alt, W. and Lauffenburger, D.A. (1987) Transient Behavior of a Chemotaxis System Modelling Certain Types of Tissue Inflammation. Journal of Mathematical Biology, 24, 691-722. [Google Scholar] [CrossRef] [PubMed]
[3] Chaplain, M.A.J. and Lolas, G. (2006) Mathematical Modelling of Cancer Invasion of Tissue: Dynamic Heterogeneity. Networks & Heterogeneous Media, 1, 399-439. [Google Scholar] [CrossRef] 
[4] Hirata, M., Kurima, S., Mizukami, M. and Yokota, T. (2017) Boundedness and Stabilization in a Two-Dimensional Two-Species Chemotaxis-Navier-Stokes System with Competitive Kinetics. Journal of Differential Equations, 263, 470-490. [Google Scholar] [CrossRef] 
[5] Hirata, M., Kurima, S., Mizukami, M. and Yokota, T. (2017) Boundedness and Stabilization in a Two-Dimensional Two-Species Chemotaxis-Navier-Stokes System with Competitive Kinetics. Journal of Differential Equations, 263, 470-490. [Google Scholar] [CrossRef] 
[6] Cao, X., Kurima, S. and Mizukami, M. (2018) Global Existence and Asymptotic Behavior of Classical Solutions for a 3D Two‐Species Chemotaxis‐Stokes System with Competitive Kinetics. Mathematical Methods in the Applied Sciences, 41, 3138-3154. [Google Scholar] [CrossRef] 
[7] Jin, H. and Xiang, T. (2019) Convergence Rates of Solutions for a Two-Species Chemotaxis-Navier-Stokes Sytstem with Competitive Kinetics. Discrete and Continuous Dynamical Systems-B, 24, 1919-1942. [Google Scholar] [CrossRef] 
[8] Cao, X., Kurima, S. and Mizukami, M. (2019) Global Existence and Asymptotic Behavior of Classical Solutions for a 3D Two-Species Keller-Segel-Stokes System with Competitive Kinetics. Funkcialaj Ekvacioj, 62, 387-408. [Google Scholar] [CrossRef] 
[9] Zheng, P., Willie, R. and Mu, C. (2020) Global Boundedness and Stabilization in a Two-Competing-Species Chemotaxis-Fluid System with Two Chemicals. Journal of Dynamics and Differential Equations, 32, 1371-1399. [Google Scholar] [CrossRef] 
[10] Zheng, P. and Willie, R. (2020) Global Weak Solutions and Eventual Smoothness in a 3D Two‐Competing‐Species Chemotaxis‐Navier‐Stokes System with Two Consumed Signals. Mathematical Methods in the Applied Sciences, 43, 3773-3785. [Google Scholar] [CrossRef] 
[11] Bousbih, H. (2019) Global Weak Solutions for a Coupled Chemotaxis Non-Newtonian Fluid. Discrete and Continuous Dynamical Systems-B, 24, 907-929. [Google Scholar] [CrossRef] 
[12] Galdi, G.P. (1994) An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Springer-Verlag. [Google Scholar] [CrossRef] 
[13] Arada, N. (2012) A Note on the Regularity of Flows with Shear-Dependent Viscosity. Nonlinear Analysis: Theory, Methods & Applications, 75, 5401-5415. [Google Scholar] [CrossRef] 

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