# American Institute of Mathematical Sciences

December  2017, 22(10): 3663-3669. doi: 10.3934/dcdsb.2017147

## Global boundedness in higher dimensions for a fully parabolic chemotaxis system with singular sensitivity

 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China

* Corresponding author

Received  December 2016 Revised  December 2016 Published  April 2017

Fund Project: Supported by the National Natural Science Foundation of China (11101060,11671066) and by the Fundamental Research Funds for the Central Universities (DUT16LK24)

In this paper we study the global boundedness of solutions to the fully parabolic chemotaxis system with singular sensitivity:$u_t=\Delta u-\chi\nabla·(\frac{u}{v}\nabla v)$, $v_t=k\Delta v-v+u$, subject to homogeneous Neumann boundary conditions in a bounded and smooth domain $\Omega\subset\mathbb{R}^{n}$ ($n\ge 2$), where $\chi, \, k>0$. It is shown that the solution is globally bounded provided $0<\chi<\frac{-(k-1)+\sqrt{(k-1)^2+\frac{8k}{n}}}{2}$. This result removes the additional restriction of $n \le 8$ in Zhao, Zheng [15] for the global boundedness of solutions.

Citation: Wei Wang, Yan Li, Hao Yu. Global boundedness in higher dimensions for a fully parabolic chemotaxis system with singular sensitivity. Discrete & Continuous Dynamical Systems - B, 2017, 22 (10) : 3663-3669. doi: 10.3934/dcdsb.2017147
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