  Orbital mean motion resonances in planetary systems originate from
dissipative processes in disk-planet interactions that lead to orbital
migration. In multi-planet systems that host giant planets, the perturbation of
the protoplanetary disk strongly affects the migration of companion planets. By
studying the well-characterized resonant planetary system around GJ 876 we aim
to explore which effects shape disk-driven migration in such a multi-planet
system to form resonant chains. We modelled the orbital migration of three
planets embedded in a protoplanetary disk using two-dimensional locally
isothermal hydrodynamical simulations. We performed a parameter study by
varying the disk thickness, $\alpha$ viscosity, mass as well as the initial
position of the planets. Moreover, we have analysed and compared simulations
with various boundary conditions at the disk's inner rim. We find that due to
the high masses of the giant planets, substantial eccentricity can be excited
in the disk. This results in large variations of the torque acting on the outer
lower-mass planet, which we attribute to a shift of Lindblad and corotation
resonances due to disk eccentricity. Depending on disk parameters, the
migration of the outer planet can be stopped in a non-resonant state. In other
models, the outer planet is able to open a partial gap and to circularize the
disk again, later entering a 2:1 resonance with the most massive planet in the
system to complete the observed Laplace resonance. Disk-mediated interactions
between planets due to spiral waves and excitation of disk eccentricity cause
deviations from smooth inward migration of exterior lower mass planets.
Self-consistent modelling of the disk-driven migration of multi-planet systems
is thus mandatory. Our results are compatible with a late migration of the
outermost planet into the resonant chain, when the giant planet pair already is
in resonance.
