Existence and boundedness of global weak solutions in three-dimensional Predator-Prey system including slow p-Laplacian diffusion dynamics

In this paper, we investigate the three-species predator-prey chemotaxis model with slow $ p $-Laplacian diffusion proposed in [16]. Under appropriate conditions on a smooth bounded domain in $ \mathbb{R}^3 $, we establish the $ L^q $-bounds on $ u_\varepsilon $ for $ q>1 $ via the Sobolev maximal regularity theory, thereby proving the existence of globally bounded weak solutions to the model for $ p>2 $, an approach that differs from the one adopted in [16]. This result refines the conclusion in [16] by weakening the condition for globally bounded weak solutions from $ p > \frac{23}{11} $ to $ p > 2 $.