  In this paper, we show that the uniform L^4-bound of the transverse Ricci
curvature along the Sasaki-Ricci flow on a compact quasi-regular transverse
Fano Sasakian (2n+1)-manifold M. When M is dimension up to seven and the space
of leaves of the characteristic foliation is well-formed, we first show that
any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to
the unique singular orbifold Sasaki-Ricci soliton on the limit space which is a
S^1-orbibundle over the unique singular Kaehler-Ricci soliton on a normal
projective variety with codimension two orbifold singularities. Secondly, for
n=1, we show that there are only two nontrivial Sasaki-Ricci solitons on a
compact quasi-regular Fano Sasakian three-sphere with its leave space a
teardrop-like and football-like space, respectively. For n=2,3, we show that
the Sasaki-Ricci soliton is trivial one if M is transverse K-stable.
