We generalized Lott-Zhang's maximal time existence of cusp Kahler-Ricci flow with superspatial initial data to arbitrary initial data with zero Lelong number.
First we construct the solution with smooth and bounded initial by perturbations. Then by Demailly's decreasing approximation method which was developed by Guedj-Zeriahi, we can construct the solution with arbitrary zero lelong number data. If time permits, we will talk about the applications on the minimal model program, especially on log canonical varieties. This work is joint with Albert Chau and Ka-Fai Li.