= Solution
For no central accretion, $A=0$ and
$$
\boxed{\bar\nu\Sigma=B r^{-1/2},\qquad v_r=0,\qquad\mathcal G=3\pi(GM_*)^{1/2}B.}
$$
This <nonaccreting constant-torque disk> has a finite inner stress and normally a nonzero inner <surface density>. An external inner <torque> supplies the <angular momentum> transported to an outer sink, although mass does not flow. If both this zero-mass-flux condition and a zero inner <torque> are imposed, $B=0$; there is no nontrivial positive-viscosity steady disk satisfying both.
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