Accretion discs with non-zero central torque

We present analytical and numerical solutions for accretion discs subject to a non-zero central torque. express this in terms of single parameter, $f$, which is the ratio outward viscous flux angular momentum from inner boundary inward advected there. The standard "accretion" disc, where condition zero-torque, represented by $f=0$. A "decretion" radial velocity at zero, $f\rightarrow\infty$. For $f > 0$ torque applied disc boundary, feeds both energy into disc. This can arise, example, case circumbinary resonances transfer binary orbits, or around rotating magnetic star allow orbits be accelerated outwards magnetospheric radius. steady-state structure as function arbitrary kinematic viscosity $\nu$. time-dependent discs, we solve equations using Green's approach specific $\nu \propto R$ provide an example solution R^{3/2}$. find that values $f\lesssim 0.1$ closely resemble discs. \gtrsim 10$ initially but sufficiently late times exhibit properties discuss application theory different astrophysical systems, particular $f$ parameter are expected cases.