This paper investigates a high-dimensional chemotaxis system with consumption of chemoattractant \begin{ eqnarray*} \left\{ \begin{ array}{ l} u_t=\Delta u-\nabla\cdot(u\nabla v), v_t=\Delta v-uv, \end{ array}\right. \end{ eqnarray*} under homogeneous boundary conditions of Neumann type, in a bounded convex domain $\Omega\subset\mathbb{ R}^n~(n\geq4)$ with smooth boundary. It is proved that if initial data satisfy $u_0\in C^0(\overline{ \Omega})$ and $v_0\in W^{ 1,q}(\Omega)$ for some $q>n$, the model possesses at least one global renormalized solution.
Categories: math.AP