In this paper, we study initial-boundary value problem of a predator-prey model with taxis strategies and a nonlinear growth rate for the predator. The global existence and uniform boundedness of positive classical solutions in any dimension are prove strictly. The results indicate that nonlinear growth rate can restrain aggregation of predator.

In this paper, we extend the gradient-dependent nonlinear sensitivity assumption of Keller-Segel-Navier-Stokes system [M. Winkler, Z. Angew. Math. Phys. 2021] to predator-prey and Keller-Segel systems in two dimensions. Under appropriate regularity assumption on the initial data, the global boundedness of classical solution is obtained.