  We carry out magnetohydrodynamic (MHD) simulations of the quasi-static
evolution and eruption of a twisted coronal flux rope under a coronal streamer
built up by an imposed flux emergence at the lower boundary. The MHD model
incorporates a simple empirical coronal heating, optically thin radiative
cooling, and field aligned thermal conduction, and thus allows the formation of
prominence condensations. We find that during the quasi-static evolution,
prominence/filament condensations of an elongated, sigmoid morphology form in
the dips of the significantly twisted field lines of the emerged flux rope due
to run-away radiative cooling. A prominence cavity also forms surrounding the
prominence, which is best observed above the limb with the line-of-sight nearly
along the length of the flux rope, as shown by synthetic SDO/AIA EUV images.
The magnetic field supporting the prominence is significantly non-force-free
despite the low plasma-beta. By comparing with a simulation that suppresses
prominence formation, we find that the prominence weight is dynamically
important and can suppress the onset of the kink instability and hold the flux
rope in equilibrium for a significantly long time, until draining of the
prominence plasma develops and lightens the prominence weight. The flux rope
eventually develops the kink instability and erupts, producing a prominence
eruption. The synthetic AIA 304 angstrom images show that the prominence is
lifted up into an erupting loop, exhibiting helical features along the loop and
substantial draining along the loop legs, as often seen in observations.
