Chemotaxis-consumption interaction: Solvability and asymptotics in general high-dimensional domains

Abstract

The basic chemotaxis-consumption model $\left(\begin{array}{c}{u}_t=\Delta u-\nabla \cdot (u\nabla v),\\ v_t=\Delta v-uv\end{array}\right)$ is considered in general, possibly non-convex bounded domains of arbitrary spatial dimension. Global existence of weak solutions is shown, along with eventual smoothness of solutions and their stabilization in the large time limit.