In this paper, we consider the following Keller&
ndash;Segel(&
ndash;Navier)&
ndash;Stokes system
where
Ω⊂RN (N=2,3) is a bounded domain with smooth boundary
dc99ce5166762e" title="Click to view the MathML source">∂Ω, κ∈R and
χ(c) is assumed to generalize the prototype
It is proved that i) for
κ≠0 and
N=2 or
κ=0 and
N∈{2,3}, the corresponding initial&
ndash;boundary problem admits a unique global classical solution which is bounded; ii) for
κ≠0 and
N=3, the corresponding initial&
ndash;boundary problem possesses at least one global weak solution.