While it is highly speculated that the first chinese CATOBAR will get a fossil fuel propulsion, I came across this message from late 2015 and wondered why no nuclear propulsion ?
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China has decades of experience in naval nuclear propulsion through their submarine program while India is still nascent in this aspect. Chosing a nuclear powered aircraft is also a long term wiser decision because it prevents some logistic hurdles, especially around fuel, especially for a carrier which will get a much more "aggressive" role.
Submarine reactors are good for about 30,000 HP. A carrier reactor need to be 3-4 times more powerful. The Soviet Navy had far deeper and broader experience with submarine nuclear reactors than the Chinese navy. But even the Soviet navy repeatedly put off designing a true surface ship reactor in order to avoid the risk. The mixed propulsion in the Kirov class semi-nuclear cruiser wasn't adopted out of some inspired compromise as some western commentators have suggested. It was adopted because the Soviets chose not to undertake to design a proper surface ship reactor, and used weak submarine reactors instead, thus necessitating an extra oil fired booster boiler for maximum power.
So for the Chinese it is prudent to use proven conventional propulsion technology with their first CTOBAR carrier in order to minimize possible delays in getting her into service.