This paper concerns global solvability of the degenerate Keller–Segel–Navier–Stokes system with flux-dependent sensitivity and superlinear signal production, \(\begin{aligned} {\left\{ \begin{array}{ll} n_t + u \cdot \nabla n= \nabla \cdot ( n^{m-1}\nabla n - n |\nabla c |^{-\alpha } \nabla c ), & x\in \Omega , \ t>0,\\ c_t + u \cdot \nabla c= \Delta c - c + n^\beta , & x\in \Omega , \ t>0,\\ u_t + (u \cdot \nabla ) u = \Delta u + \nabla P + n \nabla \Phi , \quad \nabla \cdot u = 0, & x\in \Omega , \ t>0 \end{array}\right. } \end{aligned}\) in a bounded domain \(\Omega \subset \mathbb {R}^3\) with smooth boundary, where \(m\ge 1\) , \(0<\alpha <1\) and \(\beta \ge 1\) . The main result establishes existence of global weak solutions for any suitable initial data, provided that the parameters satisfy the condition \(\begin{aligned} m> \max \left\{ \frac{(1-\alpha )(3\beta -1)+2}{3}, \,\frac{5-\alpha }{3(1+\alpha )} \right\} . \end{aligned}\)
