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$ \begin{equation*} \left\{ \begin{array}{ll} \upsilon_t = \Delta \upsilon - \chi \nabla \cdot \left( \dfrac{\upsilon}{\omega_{1}} \nabla \omega_{1} \right) + \xi \nabla \cdot \left( \dfrac{\upsilon}{\omega_{2}} \nabla \omega_{2} \right), & x \in \Omega, \\ 0 = \Delta \omega_{1} - \omega_{1} + \upsilon, & x \in \Omega, \\ \omega_{2t} = \Delta \omega_{2} - \upsilon^{\gamma} \omega_{2}, & x \in \Omega, \end{array} \right. \end{equation*} $where the domain $ \Omega $ is a smoothly bounded set in $ \mathbb{R}^n $ ($ n \ge 2 $) and the parameters satisfy $ \chi, \xi, \gamma > 0 $. It has been proven that if $ \chi < \frac{1}{n} $ and $ \gamma < \frac{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 $ \chi $ and $ \xi $ to satisfy a repulsion dominance relationship to prevent blow-up, our result shows that the nonlinear dissipation term effectively releases this inherent constraint between $ \chi $ and $ \xi $.