  In bounded smooth domains $\Omega\subset\mathbb{R}^N$, $N\in\{2,3\}$, we
consider the Keller-Segel-Stokes system \begin{align*}
  n_t + u\cdot \nabla n &= \Delta n - \chi \nabla \cdot(\frac{n}{c}\nabla c),\\
c_t + u\cdot \nabla c &= \Delta c - c + n,\\ u_t &= \Delta u + \nabla P +
n\nabla \phi, \qquad \nabla \cdot u=0, \end{align*} and prove global existence
of generalized solutions if \[
  \chi<\begin{cases}
  \infty,&N=2,\\ \frac{5}{3},&N=3.
  \end{cases} \] These solutions are such that blow-up into a persistent
Dirac-type singularity is excluded.
