Global boundedness in a chemotaxis-Stokes system with nonlinear diffusion mechanism involving gradient dependent flux limitation and indirect signal production

This paper is concerned with the Keller-Segel-Stokes system { n(t) + u <middle dot> Vn = Delta n(m)- V <middle dot> (nf(|Vv|(2))Vv), v(t )+u<middle dot>Vv= Delta v -v + w, w(t) +u<middle dot>Vw= Delta w -w + n, u(t) = Delta u + VP + nV phi, V <middle dot> u = 0, under no-flux/no-flux/no-flux/Dirichlet boundary conditions in a smoothly bounded domain Omega C R-3, with given suitably regular functions f and phi, as well as f satisfies f(xi) <= Kf(1 + xi)(- alpha /2) , xi >= 0 and Kf > 0. It is shown that for all suitably regular initial data the associated initial-boundary value problem possesses at least one globally bounded weak solution provided 9m + 4 alpha > 10. Our result strictly proved that the volume saturation effect is indeed conductive to the global existence and boundedness of the three-dimensional Keller-Segel-Stokes system. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.