Global boundedness of the chemotaxis system with weakly singular sensitivity and nonlocal term in any dimension

This paper is concerned with the parabolic-elliptic chemotaxis system involving weakly singular sensitivity and a nonlocal source: $u_t=Δu-χ\nabla\cdot\left(\frac{u}{v^k}\nabla v\right) +u^α\left(r-μ\int_Ωu^β\,dx\right)$ and $0=Δv-v+u^γ$ under homogeneous Neumann boundary conditions in a smooth boun