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

Gradient Shrinking Sasaki-Ricci Solitons on Sasakian Manifolds of Dimension Up to Seven