Electronic Journal of Differential Equations,
Vol. 2019 (2019), No. 38, pp. 1-19.

Title: Renormalized solutions to a chemotaxis system with consumption of chemoattractant

Authors: Hengling Wang (Southeast Univ., Nanjing, China)
         Yuxiang Li.   (Southeast Univ., Nanjing, China)
 
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