  We study the Lindbladian dynamics of the Sachdev-Ye-Kitaev (SYK) model, where
the SYK model is coupled to Markovian reservoirs with jump operators that are
either linear or quadratic in the Majorana fermion operators. Here, the linear
jump operators are non-random while the quadratic jump operators are sampled
from a Gaussian distribution. In the limit of large $N$, where $N$ is the
number of Majorana fermion operators, and also in the limit of large $N$ and
$M$, where $M$ is the number of jump operators, the SYK Lindbladians are
analytically tractable, and we obtain their stationary Green's functions, from
which we can read off the decay rate. For finite $N$, we also study the
distribution of the eigenvalues of the SYK Lindbladians.
