Can a chemotaxis-consumption system recover from a measure-type aggregation state in arbitrary dimension?

We consider the chemotaxis-consumption system $$\{\begin{array}{rl}{\displaystyle u_t}& {\displaystyle =\mathrm{\Delta }u-\chi \mathrm{\nabla }\cdot (u\mathrm{\nabla }v)}\\ {\displaystyle v_t}& {\displaystyle =\mathrm{\Delta }v-uv}\end{array}$$ in a smooth bounded domain $\mathrm{\Omega }\subseteq {\mathbb{R}}^n$, $n\ge 2$, with parameter $\chi >0$ and Neumann boundary conditions. It is well known that, for sufficiently smooth nonnegative initial data and under a smallness condition for the initial state of $v$, solutions of the above system never blow up and are even globally bounded. Going in a sense a step further in this paper, we ask the question whether the system can even recover from an initial state that already resembles measure-type blowup. To answer this, we show that, given an arbitrarily large positive Radon measure $u_0$ with $u_0(\bar{\mathrm{\Omega }})>0$ as the initial data for the first equation and a nonnegative $L^{\mathrm{\infty }}(\mathrm{\Omega })$ function $v_0$ with $$0<\mathrm{\parallel }{v}_0{\mathrm{\parallel }}_{L^{\mathrm{\infty }}(\mathrm{\Omega })}<\frac{2}{3n\chi }$$ as initial data for the second equation, it is still possible to construct a global classic solution to the above system.