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 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 runaway radiative cooling. A prominence cavity also forms around 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 weight of the prominence 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 reduces the weight of the prominence. 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 is often seen in observations.
