Boundedness in a chemotaxis-fluid system involving a gradient-dependent flux limitation and indirect signal production mechanism

This paper is concerned with the Keller-Segel-Stokes system {n(t) + u center dot del v = Delta n - del center dot (ng (vertical bar del v vertical bar(2)) del v), v(t) + u center dot del v = Delta v - v + w, w(t) + u center dot del w = Delta w - w + n, (*) u(t) = Delta u + del P + n del phi , del center dot u = 0, under no-flux/no-flux/no-flux/Dirichlet boundary conditions in smoothly bounded domains Omega subset of R-3, with given suitably regular functions f and phi, as well as f satisfies f (|del v|(2)) < K-f (1 + |del v|(2))(-alpha/2). It is shown that for all suitably regular initial data an associated initial-boundary value problem (*) possesses a globally defined bounded classical solution provided alpha > 1/4. We underline that the same results were established for the corresponding system with direct signal production in a well-known result if alpha > 1/2 in [50]. Our result rigorously confirms that the indirect signal production mechanism genuinely contributes to the global solvability of the three-dimensional Keller-Segel-Stokes system. (c) 2023 Elsevier Inc. All rights reserved.