  We consider the Keller-Segel system of consumption type coupled with an
incompressible fluid equation. The system describes the dynamics of oxygen and
bacteria densities evolving within a fluid. We establish local well-posedness
of the system in Sobolev spaces for partially inviscid and fully inviscid
cases. In the latter, additional assumptions on the initial data are required
when either the oxygen or bacteria density touches zero. Even though the oxygen
density satisfies a maximum principle due to consumption, we prove finite time
blow-up of its $C^{2}$--norm with certain initial data.
