| Abstract: |
| Motivated by the study of bacteria`s response to environmental conditions, we consider the doubly degenerate nutrient taxis system governed by $
u_t = \nabla \cdot ( uv \nabla u) - \nabla\cdot (u^{\alpha} v\nabla v) + uv$ and $
v_t = \Delta v - u v$, where
$\alpha \in [0,2]$ is the bacterial response parameter. Global weak solvability is highly challenging due to both the doubly degenerate diffusion and the strong chemotactic effect; we establish this for $0 \leq \alpha < 2$, see https://arxiv.org/pdf/2508.03268. |
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