The Chinese already have their third carrier under construction, they just haven't made an official news release about it yet.
The satellite photos show something very similar to a Nimitz carrier, just a little smaller. It's expected to have catapults, no one is yet sure about nuclear power. I think it will still be conventionally powered, the nuclear power will come in the fourth or fifth carrier they build. Yes, everyone is sure the Chinese will be building many more as the shipyard that they are building these carriers in is being tripled in size.
The first two carriers are simply training ships, needed to figure out how to sail a carrier, how to do flight operations at all, train escort ships & subs that are typically part of a carrier task force. The third one will also be mostly a training ship, needed to train in how to do catapult flight operations. It''s expected that the fourth carrier will be the first one intended to be a combat vessel, but I am betting it will be nuclear powered and also mostly used as a training ship at first - teaching crews how to run a nuclear reactor powered ship. Then after the Chinese build several more it will join it's sisters in being a combat ship.