Electron. J. Differential Equations, Vol. 2019 (2019), No. 38, pp. 1-19.

Renormalized solutions to a chemotaxis system with consumption of chemoattractant

Hengling Wang, Yuxiang Li

Abstract:
This article concerns the high-dimensional chemotaxis system with consumption of chemoattractant
$$\displaylines{ u_t=\Delta u-\nabla\cdot(u\nabla v),\cr v_t=\Delta v-uv, }$$
under homogeneous boundary conditions of Neumann type, in a bounded domain $\Omega\subset\mathbb{R}^n~(n\geq 4)$ with smooth boundary. We prove that that if the initial data satisfy $u_0\in C^0(\overline{\Omega})$ and $v_0\in W^{1,q}(\Omega)$ for some $q>n$, this model possesses at least one global renormalized solution.

Submitted May 19, 2018. Published March 11, 2019.
Math Subject Classifications: 35A01, 35K57, 35Q92, 92C17
Key Words: Keller-Segel model; renormalized solutions; entropy method

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Hengling Wang
Institute for Applied Mathematics
School of Mathematics, Southeast University
Nanjing 211189, China
email: hlwang@seu.edu.cn
Yuxiang Li
Institute for Applied Mathematics
School of Mathematics
Southeast University
Nanjing 211189, China
email: lieyx@seu.edu.cn

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