Global existence and boundedness in a two-dimensional self-consistent chemotaxis-Navier-Stokes system

Global existence and boundedness in a two-dimensional self-consistent chemotaxis-Navier-Stokes system | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 7 November 2025 V1 Latest version Share on Global existence and boundedness in a two-dimensional self-consistent chemotaxis-Navier-Stokes system Authors : Zhibin Hu , Huijuan Song 0000-0002-5031-453X [email protected] , and jiashan zheng 0000-0002-1304-9853 Authors Info & Affiliations https://doi.org/10.22541/au.176253850.05057256/v1 241 views 160 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In this paper, we investigate an initial-boundary value problem for the self-consistent chemotaxis-Navier-Stokes system { n t + u · ∇ n = ∆ n − ∇ · ( n ( 1 + n ) − α ∇ c ) + ∇ · ( n ∇ ϕ ), x ∈ Ω, t > 0, c t + u · ∇ c = ∆ c − c + n, x ∈ Ω, t > 0, u t + κ ( u · ∇ ) u + ∇ P = ∆ u − n ∇ ϕ + n ( 1 + n ) − α ∇ c, x ∈ Ω, t > 0, ∇ · u = 0, x ∈ Ω, t > 0, where Ω ⊂ R 2 is a bounded domain with smooth boundary, α> 0, κ ∈R and the gravitational potential function ϕ ∈ W 2, ∞ ( Ω ) . The novelty of this work lies in the consideration of both the effect of gravity (potential force) on cells and the influence of chemotactic force on the fluid, resulting in a stronger coupling mechanism than that observed in the usual chemotaxis-Navier-Stokes model studied in most existing literatures. It is shown that if α > 1 4, then for any sufficiently regular initial data, this system admits at least one global and bounded solution to this system under no-flux boundary conditions for n , c and homogeneous Dirichlet boundary condition for u . Our analytic approach is based on a new energy-like functional ∫ Ω n 1 + k 0 α + ∫ Ω | ∇ c | 2 with some integer k 0 > 3 α . Supplementary Material File (manucript-1105(1).pdf) Download 481.69 KB Information & Authors Information Version history V1 Version 1 07 November 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords boundedness chemotaxis-navier-stokes system global solvability self-consistent signal production Authors Affiliations Zhibin Hu Jiangxi Normal University View all articles by this author Huijuan Song 0000-0002-5031-453X [email protected] Jiangxi Normal University View all articles by this author jiashan zheng 0000-0002-1304-9853 Yantai University View all articles by this author Metrics & Citations Metrics Article Usage 241 views 160 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Zhibin Hu, Huijuan Song, jiashan zheng. Global existence and boundedness in a two-dimensional self-consistent chemotaxis-Navier-Stokes system. Authorea . 07 November 2025. DOI: https://doi.org/10.22541/au.176253850.05057256/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. 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