Global boundedness in a 3D quasilinear Keller-Segel-Stokes system with nonlinear sensitivity and indirect signal production

under no-flux/no-flux/no-flux/Dirichlet boundary conditions in smoothly bounded domains & omega; C R3 with m > 0 and & alpha; E R. It is shown that for all suitably regular initial data an associated initial-boundary value problem (*) possesses at least one global boundedness weak solution provided m +& alpha; > 109 . We underline that the same results were established for the corresponding system with direct signal production in a well-known result if m + 2 & alpha; > 2 and m > 34 in [24] or m > 43 and & alpha; = 0 in [61] or m = 1 and & alpha; > 13 in [51]. Our result rigorously confirms that the indirect signal production mechanism genuinely contributes to the global solvability of the three-dimensional Keller-Segel-Stokes system.& COPY; 2023 Elsevier Masson SAS. All rights reserved.