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In this paper, we consider the following indirect signal generation and singular sensitivity  n t = Δ n + χ ∇ ⋅ n / φ c ∇ c ,   x ∈ Ω , t &gt; 0 , c t = Δ c − c + w ,   x ∈ Ω , t &gt; 0 , w t = Δ w − w + n ,   x ∈ Ω , t &gt; 0 , in a bounded domain  Ω ⊂ R N N = 2 , 3 with smooth boundary  ∂ Ω . Under the nonflux boundary conditions for  n ,  c , and  w , we first eliminate the singularity of  φ c by using the Neumann heat semigroup and then establish the global boundedness and rates of convergence for solution.

Boundedness and Asymptotic Behavior to a Chemotaxis System with Indirect Signal Generation and Singular Sensitivity