(untitled) (Journal of Mathematical Study, 2025)
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. Then we are able to study the structure of the limit space. As consequences, when M is of dimension five and the space of leaves of the characteristic foliation is of type I, any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold Sasaki-Ricci soliton and is trivial one if M is transverse K-stable. Note that when the characteristic foliation is of type II, the same estimates hold along the conic Sasaki-Ricci flow.