In this work, we consider the following Keller–Segel–Navier–Stokes system with density-suppressed motility and nutrient consumption \(\begin{aligned} \left\{ \begin{aligned} \rho _t + \textbf{u}\cdot \nabla \rho&= \Delta \left( \rho \gamma (h)\right) +\rho f(n),&\qquad x\in \Omega ,\, t>0,\\ h_t + \textbf{u}\cdot \nabla h&= \Delta h-h+\rho ,&\qquad x\in \Omega ,\, t>0,\\ n_t + \textbf{u}\cdot \nabla n&= \Delta n-\rho f(n),&\qquad x\in \Omega ,\, t>0,\\ \textbf{u}_t + (\textbf{u}\cdot \nabla ) \textbf{u}&= \Delta \textbf{u}+\nabla P+\rho \nabla \Phi ,&\qquad x\in \Omega ,\, t>0,\\ \nabla \cdot \textbf{u}&=0,&\qquad x\in \Omega ,\, t>0 \end{aligned} \right. \end{aligned}\) in a bounded domain \(\Omega \subset {\mathbb {R}}^2\) with smooth boundary under the no-flux boundary conditions for \(\rho \) , h, n and the Dirichlet boundary condition for \(\textbf{u}\) . We showed that for general (large) regular initial data, the corresponding initial-boundary value problem possesses a global generalized solution. In particular, we proved these generalized solutions will eventually become smooth under the smallness assumption on the initial mass \(\left\| \rho (\cdot ,0)+n(\cdot ,0)\right\| _{L^{1}(\Omega )}\) .
