This paper considers the power-type singular chemotaxis-fluid system with indirect signal consumption and logistic source. \(\begin{aligned} \left\{ \begin{array}{llll} & n_{t}+u\cdot \nabla n=\Delta n -\chi \nabla \cdot (\frac{n}{v^{\alpha }}\nabla v)+rn-\mu n^2,& & x\in \Omega ,t> 0,\\ & v_{t}+u\cdot \nabla v=\Delta v-vw,& & x\in \Omega ,t> 0,\\ & w_{t}+u\cdot \nabla w= \Delta w-w+n,& & x\in \Omega ,t> 0,\\ & u_t+(u\cdot \nabla )u=\Delta u-\nabla P+n\nabla \Phi ,\qquad \nabla \cdot u=0,& & x\in \Omega ,t> 0\\ \end{array} \right. \end{aligned}\) in a smoothly bounded domain \(\Omega \in \mathbb {R}^2\) , where \(r\in \mathbb {R}\) , \(\mu ,\chi >0\) and \(\Phi \in W^{2, \infty }(\Omega )\) . For any \(\mu , \alpha >0\) , we proved that the system possesses a global classical solution, which is uniformly bounded. For the case of \(\alpha =1\) , we point out that the global existence of classical solution was proved on the corresponding system without logistic source. In comparison with this result, our result apparently confirms that quadratic degradation is authentically capable of precluding the blow-up of the two-dimensional chemotaxis-fluid system with singular sensitivity and indirect signal consumption. Moreover, in the situation of direct signal consumption and \(\alpha =1\) , it is asserted that the global boundedness of classical solution was obtained on the associated system for a appropriately large \(\mu >0\) . Contrasted with this result, our result obviously can illustrate that the the indirect signal consumption mechanism is favorable for the global boundedness of the two-dimensional chemotaxis-fluid system with power-type singular sensitivity and logistic source.
