In this paper, we consider the following Keller–Segel(–Navier)–Stokes system
where
Ω⊂RN (N=2,3) is a bounded domain with smooth boundary
∂Ω, κ∈R and
a07b2039b64b35da5153f5b1a9c7ca84" title="Click to view the MathML source">χ(c) is assumed to generalize the prototype
It is proved that i) for
43a821816fe4381b" title="Click to view the MathML source">κ≠0 and
N=2 or
κ=0 and
N∈{2,3}, the corresponding initial–boundary problem admits a unique global classical solution which is bounded; ii) for
43a821816fe4381b" title="Click to view the MathML source">κ≠0 and
N=3, the corresponding initial–boundary problem possesses at least one global weak solution.