  In this paper we examine the issue of characterizing the transport associated
with gravitational instabilities in relatively cold discs, discussing in
particular under which condition it can be described within a local, viscous
framework. We present the results of global, three-dimensional, SPH simulations
of self-gravitating accretion discs, in which the disc is cooled using a simple
parameterization for the cooling function. Our simulations show that the disc
settles in a ``self-regulated'' state, where the axisymmetric stability
parameter $Q\approx 1$ and where transport and energy dissipation are dominated
by self-gravity. We have computed the gravitational stress tensor and compared
our results with expectations based on a local theory of transport. We find
that, for disc masses smaller than $0.25M_{\star}$ and aspect ratio
$H/r\lesssim 0.1$, transport is determined locally, thus allowing for a viscous
treatment of the disc evolution.

Astrophysics