  Theoretical and numerical studies have shown that large-scale vortices in
Protoplanetary discs can result from various hydrodynamical instabilities. Once
produced, such vortices can survive nearly unchanged over a large number of
rotation periods, slowly migrating towards the star. In the outer disc,
self-gravity may affect the vortex evolution and must be included in models.
  We performed 2D hydrodynamic simulations using the RoSSBi3D code. The outline
of our computations was limited to Euler's equations assuming a non-homentropic
and non-adiabatic flow for an ideal gas. A series of 45 runs were carried out
starting from a Gaussian vortex-model; the evolution of vortices was followed
during 300 orbits for various values of the vortex parameters and the Toomre
parameter. Two simulations, with the highest resolution (HR) thus far for
studies of vortices, were also run to better characterise the internal
structure of the vortices and for the purpose of comparison with an isothermal
case.
  We find that SG tends to destabilise the injected vortices, but compact
small-scale vortices seem to be more robust than large-scale oblong vortices.
Vortex survival critically depends on the value of the disc's Toomre parameter,
but may also depend on the disc temperature at equilibrium. Disc SG must be
small enough to avoid destruction in successive splitting and an approximate
`stability' criterion is deduced for vortices. The self-gravitating vortices
that we found persist during hundreds of rotation periods and look like the
quasi-steady vortices obtained in the non-self-gravitating case. A number of
these self-gravitating vortices are eventually accompanied by a secondary
vortex with a horseshoe motion. These vortices reach a new rotational
equilibrium in their core, tend to contract in the radial direction, and spin
faster.
