Title: Singular sensitivity in a Keller-Segel-fluid system,
Abstract: In bounded smooth domains $\Omega\subset\mathbb{R}^N$, $N\in\{2,3\}$,
considering the chemotaxis--fluid system
\[ \begin{cases} \begin{split} & n_t + u\cdot \nabla n &= \Delta n - \chi
\nabla \cdot(\frac{n}{c}\nabla c) &\\ & c_t + u\cdot \nabla c &= \Delta c - c +
n &\\ & u_t + \kappa (u\cdot \nabla) u &= \Delta u + \nabla P + n\nabla \Phi &
\end{split}\end{cases} \] with singular sensitivity, we prove global existence
of classical solutions for given $\Phi\in C^2(\bar{\Omega})$, for $\kappa=0$
(Stokes-fluid) if $N=3$ and $\kappa\in\{0,1\}$ (Stokes- or Navier--Stokes
fluid) if $N=2$ and under the condition that \[
0<\chi<\sqrt{\frac{2}{N}}. \]