  In this work, we study the no-flux initial-boundary value problem for the
doubly degenerate nutrient taxis system \begin{align}
\begin{cases}\tag{$\star$}\label{eq 0.1} u_t=\nabla \cdot(u v \nabla u)-\chi
\nabla \cdot\left(u^{2} v \nabla v\right)+\ell u v, & x \in \Omega, t>0, \\
v_t=\Delta v-u v, & x \in \Omega, t>0 \end{cases} \end{align} in a smoothly
bounded convex domain $\Omega \subset \mathbb{R}^2$, where $\chi>0$ and $\ell
\geq 0$. In this paper, we present that for all reasonably regular initial
data, the model \eqref{eq 0.1} possesses a global bounded weak solution which
is continuous in its first and essentially smooth in its second component.
\end{abstract}
