A dimension-independent critical exponent in a nutrient taxis system

Michael Winkler

In a ball $\hat{I}\text{c◯}\subset R^n$ with arbitrary $n\ge 1$, the chemotaxis-consumption system \[ \left\{ \begin{array}{l} u_t = \nabla \cdot \big(D(u)\nabla u\big) - \nabla \cdot (u\nabla v…