Singular sensitivity-driven chemotaxis models with nonlinear dissipation: Global existence under attraction-repulsion effects

In this paper, we investigate an attraction-repulsion chemotaxis system with singular sensitivitiesunder no-flux boundary conditions$ {equation*} \{ {array}{ll} υ_t = Δ υ - χ ∇ · ( {υ}{ω₁} ∇ ω₁ ) + ξ ∇ · ( {υ}{ω₂} ∇ ω₂ ), & x ∈ Ω, \\ 0 = Δ ω₁ - ω₁ + υ, & x ∈ Ω, \\ ω₂ₜ = Δ ω₂ - υγ ω₂, & x ∈ Ω, {array} . {equation*} $where the domain $ Ω $ is a smoothly bounded set in $ R^n $ ($ n ≥ 2 $) and the parameters satisfy $ χ, ξ, γ > 0 $. It has been proven that if $ χ < 1/n $ and $ γ < 2/n+2, $ then the system admits a global classical solution. Unlike classical attraction-repulsion models such as those in [11,36], which require the sensitivity coefficients $ χ $ and $ ξ $ to satisfy a repulsion dominance relationship to prevent blow-up, our result shows that the nonlinear dissipation term effectively releases this inherent constraint between $ χ $ and $ ξ $.