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.