We performed a series of hydrodynamic simulations to investigate the orbital evolution of a Jovian planet embedded in a protostellar disk. In order to take into account of the effect of the disk's self-gravity, we developed and adopted an ANTARES code which is based on a 2D Godunov scheme to obtain the exact Reimann solution for isothermal or polytropic gas, with nonreflecting boundary conditions. Our simulations indicate that in the study of runaway (type Ⅲ) migration it is important to carry out a fully self-consistent treatment of the gravitational interaction between the disk and the embedded planet. Through a series of convergence tests, we show that adequate numerical resolution, especially within the planet's Roche lobe, critically determines the outcome of the simulations. We consider a variety of initial conditions and show that isolated, noneccentric protoplanets do not undergo type Ⅲ migration. We attribute the difference between our and previous simulations to the contribution of a self-consistent representation of the disk's self-gravity. Nevertheless, type Ⅲ migration cannot be completely suppressed, and its onset requires finite-amplitude perturbations such as that induced by planet-planet interaction. We determine the radial extent of type Ⅲ migration as a function of the disk's self-gravity.
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