The bad news first. The Peoples Republic of China now believes that it can successfully prevent the United States from intervening in the event of a Chinese invasion of Taiwan or some other military assault by Beijing.
Uh, that is because it can do just that. Note that it does not claim China believes it can defeat the U.S. in a war, only that it can deploy sufficient resources in a short enough period of time that America will simply have no choice but to let events play out rather than directly intervening. In that respect I certainly do believe China has the military capacity to achieve a rapid series of successes against Taiwanese forces. They could easily take out Taiwan's fleet, which is mostly crap save for the Kidd destroyers, and their air force is pretty decrepit as well. Compared to China, which has most of the latest bobs and whistles, Taiwan is like Iraq going up against the United States. I imagine the Chinese have studied the implications of conflicts like the Persian Gulf War for an attack on Taiwan very closely. Taiwan would find itself unable to defend its waters and airspace within a day. A rapid series of airstrikes using an array of precision-guided munitions could wipe out most of Taiwan's air defense structure in 24 hours and its navy would be even easier to dispense with than that. From that moment on, China can erect a total air and naval blockade over the main island and seize the smaller islands with ease. A land invasion would be the trickiest part, but exactly how much will the people of Taiwan will have to resist is uncertain. If they realize the U.S. is not coming to save them, many may prefer preventing the economic devastation and loss of life that would result from a lengthy resistance campaign and see if they can instead negotiate favorable terms for reunification.
Newsflash #2.... North Korea could conquer South Korea and annihilate the US presence there as well.
Um, no, actually. I do think North Korea could cause massive destruction to South Korea through a variety of military measures if it strikes first, but the ROK's military capabilities are far greater than North Korea's. They would have to use nukes to stand a chance and I am not even sure that would make a difference, but they will not be able to prevent international intervention if they try such a thing. China will take care of Pyongyang itself in that scenario.
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Question: What kind of amphibious landing capabilities do the Chinese have?
They have three modern LPDs each capable of carrying over 500 troops at a time with several more being built, dozens of older and lower tech LSTs that could each carry a few hundred troops, and they have several Zubr-class air-cushioned landing crafts that are fully capable of making a round trip from one side of the Strait to another with fuel to spare in just four hours and can carry as many as 500 troops. You then have to consider their ability to deploy paratroopers, which as far back as 1988 was said to be capable of deploying 10,000 troops to any part of China in a matter of days. Exactly how many troops they could deploy in a matter of days with all their resources in play is unclear, though it is likely they could get at least 20,000 soldiers on Taiwan in the first 48 hours, most likely more as with total air and naval dominance in this age it would be much easier to establish a beachhead and from that point they can just use any means at their disposal to reinforce their position on the main island. Mind you, all the little islands would likely be taken in this initial period of conflict, including the Penghu islands.
One potential source of conflict in the event of a war with Taiwan are the current holdings they have in the South China Sea. I have no doubt the PRC would be looking to take Taiping island in the Spratly Island chain and it would be quite the prize to have for any power in the region. Vietnam and the Philippines would not be pleased with that result, though.