Regularizing property of the twisted conical K\"ahler-Ricci flow

In this paper, we show the regularity and uniqueness of the twisted conical K\"ahler-Ricci flow running from a positive closed current with zero Lelong number, which extends the regularizing property of the smooth twisted K\"ahler-Ricci flow, known as Guedj-Zeriahi's existence theorem and Di Nezza-Lu's uniqueness theorem, to the conical singularity case.