Global solvability and boundedness to a attraction–repulsion model with logistic source

In this paper, we deal with an attraction–repulsion model with a logistic source as follows: { u t = Δ u − χ ∇ ⋅ ( u ∇ v ) + ξ ∇ ⋅ ( u ∇ w ) + μ u q ( 1 − u ) in Q , v t = Δ v − α 1 v + β 1 u in Q , w t = Δ w − α 2 w + β 2 u in Q , where Q = Ω × R + , Ω ⊂ R 3 is a bounded domain. We mainly focus on the influence of logistic damping on the global solvability of this model. In dimension 2, q can be equal to 1 (Math. Methods Appl. Sci. 39(2):289–301, 2016 ). In dimension 3, we derive that the problem admits a global bounded solution when q > 8 7 . In fact, we transfer the difficulty of estimation to the logistic term through iterative methods, thus, compared to the results in (J. Math. Anal. Appl. 2:448 2017 ; Z. Angew. Math. Phys. 73(2):1–25 2022 ) in dimension 3, our results do not require any restrictions on the coefficients.