Solution
= Solution
For a <zero-torque inner boundary condition> at finite $r_{\rm in}$,
$$
\boxed{\bar\nu\Sigma=\frac{\dot M}{3\pi}\left(1-\sqrt{\frac{r_{\rm in}}r}\right).}
$$
With positive finite inner <kinematic viscosity>, $\Sigma$ tends to zero there. At fixed nonzero inward mass flux, the corresponding $v_r=-\dot M/(2\pi r\Sigma)$ becomes large, signaling the breakdown of the nearly circular <thin disc> approximation in the inner transition region.