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In this study, we investigate the two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity:ut=∇⋅(uθ−1∇u)−χ∇⋅uv∇v,x∈Ω,t&gt;0,vt=Δv−v+u+g(x,t),x∈Ω,t&gt;0,(∗)\left\{\begin{array}{ll}{u}_{t}=\nabla \cdot \left({u}^{\theta -1}\nabla u)-\chi \nabla \cdot \left(\frac{u}{v}\nabla v\right),&amp; x\in \Omega ,\hspace{0.33em}t\gt 0,\\ {v}_{t}=\Delta v-v+u+g\left(x,t),&amp; x\in \Omega ,\hspace{0.33em}t\gt 0,\\ \end{array}\right.\hspace{2.0em}\hspace{2.0em}\hspace{2.0em}\left(\ast )in a bounded domain with smooth boundary. We present the global boundedness of weak solutions to the model (∗\ast) ifθ&gt;32\theta \gt \frac{3}{2}and ( 1.10 )–( 1.11 ). This result improves our recent work.

Global boundedness in a two-dimensional chemotaxis system with nonlinear diffusion and singular sensitivity