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This manuscript deals with the three-dimensional version of a flux-limitedKeller-Segel system coupled to the incompressible Stokes equations throughtransport and buoyancy.  The main goal consists in verifying that within a certain parameter regime,known as being optimal therefor in some fluid-free simplification, a feature ofblow-up prevention by suitably strong flux limitation persists also in theframework of the considered full chemotaxis-fluid system. To achieve this, as asecondary objective of possibly independent interest the manuscript separatelyestablishes some conditional bounds for fluid fields and taxis gradients in afairly general setting.  The application thereof to the specific problem under considerationthereafter facilitates the derivation of a result on global existence ofbounded classical solutions for widely arbitrary initial data actually, indeedwithin the entire and essentially optimal parameter range, through an argumentwhich appears to be signficantly condensed when compared to reasonings pursuedin previous related works.

Conditional estimates in three-dimensional chemotaxis-Stokes systems and  application to a Keller-Segel-fluid model accounting for gradient-dependent  flux limitation