= Ratio time change for a homogeneous fluid model
{title2=$du/dt=1/s$}
For a two-coordinate <fluid model> with $\dot s=g(n/s)$, $\dot n=f(n/s)$ and $s>0$, set $\kappa=n/s$ and $du/dt=1/s$. Then $d\kappa/du=f(\kappa)-\kappa g(\kappa)$ and $d\log s/du=g(\kappa)$. A bounded ratio eventually confined where $g\leq-\eta<0$ makes $s$ decay exponentially in the new time. Since $dt/du=s$, the original fluid time has a finite terminal value and both coordinates tend to zero. This is a useful <finite-time draining of a fluid model> argument; the singular origin is treated by a stopped trajectory.
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