In this work, we study the doubly degenerate nutrient taxis system with logistic source \(\begin{aligned} {\left\{ \begin{array}{ll} u_t=\nabla \cdot (u^{l-1} v \nabla u)- \nabla \cdot \left( u^{l} v \nabla v\right) + u - u^2, \\v_t=\Delta v-u v \end{array}\right. } \end{aligned}\) in a smooth bounded domain \(\Omega \subset \mathbb {R}^2\) , where \(l \geqslant 1\) . It is proved that for all reasonably regular initial data, the corresponding homogeneous Neumann initial-boundary value problem possesses a global weak solution which is continuous in its first and essentially smooth in its second component.
