Global boundedness in the higher-dimensional fully parabolic chemotaxis with weak singular sensitivity and logistic source

We consider the following chemotaxis system under homogeneous Neumann boundary conditions in a smooth, open, bounded domain Ω ⊂ Rⁿ with n ≥ 3: {equation*} {cases} u_t = Δ u - χ ∇ · ( u/v^k ∇ v ) + ru - μ u^2, & in Ω × (0,Tₘₐₓ), v_t = Δ v - α v + β u, & in Ω × (0,Tₘₐₓ), {cases} {equation*} where k ∈ (0,1), and χ, r, μ, α, β are positive parameters. In this paper, we demonstrate that for suitably smooth initial data, the problem admits a unique nonnegative classical solution that remains globally bounded in time when μ is sufficiently large.