  We carry out a series of high resolution ($1024\times 1024$) hydrodynamical
simulations to investigate the orbital evolution of Jupiter and Saturn embedded
in a gaseous protostellar disk. Our work extends the results in the classical
papers of Masset & Snellgrove (2001) and Morbidelli & Crida (2007) by exploring
various surface density profiles ($\sigma$), where $\sigma \propto
r^{-\alpha}$. The stability of the mean motion resonances(MMRs) caused by the
convergent migration of the two planets is studied as well. Our results show
that:(1) The gap formation process of Saturn is greatly delayed by the tidal
perturbation of Jupiter. These perturbations cause inward or outward runaway
migration of Saturn, depending on the density profiles on the disk. (2) The
convergent migration rate increases as $\alpha$ increases and the type of MMRs
depends on $\alpha$ as well. When $0<\alpha<1$, the convergent migration speed
of Jupiter and Saturn is relatively slow, thus they are trapped into 2:1 MMR.
When $\alpha>4/3$, Saturn passes through the $2:1$ MMR with Jupiter and is
captured into the $3:2$ MMR. (3) The $3:2$ MMR turns out to be unstable when
the eccentricity of Saturn ($e_s$) increases too high. The critical value above
which instability will set in is $e_s \sim 0.15$. We also observe that the two
planets are trapped into $2:1$ MMR after the break of $3:2$ MMR. This process
may provide useful information for the formation of orbital configuration
between Jupiter and Saturn in the Solar System.
