  In this paper, we study the consumption-chemotaxis-Stokes model with porous
medium slow diffusion in a three dimensional bounded domain with zero-flux
boundary conditions and no-slip boundary condition. In recent ten years, many
efforts have been made to find the global bounded solutions of
chemotaxis-Stokes system in three dimensional space. Although some important
progress has been carried out in some papers, as mentioned by some authors, the
question of identifying an optimal condition on m ensuring global boundedness
in the three-dimensional framework remains an open challenge. In the present
paper, we put forward a new estimation technique, completely proved the
existence of global bounded solutions for arbitrary slow diffusion case, and
partially answered the open problem proposed by Winkler.
