How do those who understand Noah's Flood to be a global flood explain what the carnivorous animals ate after disembarking, if there were only 2 of all the other species left? Eating 1 would stop those species' reproductive lines, so what happened here?
This is probably best answered by this article, but for the sake of having an Answer here...
First off, I want to take an aside to address a point that unbelievers often raise; namely, that there's no way Noah could take two of each of thousands of species of animal and have enough food for them.
That isn't what Scripture actually says, though it's easy to see where a layperson might be confused. There were not two of every species of animal on the Ark; there were two of every kind of animal. "Species" is a relatively recent, and very poorly defined delineation. Scripturally speaking, animals reproduce according to their kind. Lions and housecats can interbreed (at least through intermediaries), and are therefore the same kind (some Creation scientists like to use the term baramin). Same with wolves and dingoes, horses and zebras, and many others. Therefore, Noah only needed two of the cat kind (and likely those would have been closer to the size of servals than tigers). Conservative but realistic estimates place the number of animals (many of which were likely quite small) at less than ten thousand. Some calculations have estimated that the Ark could hold hundreds of thousands of animals the size of sheep (which are well above median size). Even with this latter figure likely assuming fairly crowded conditions with no food storage, it's easy to see that the problem is nowhere near as difficult as scoffers try to make it out to be. This article goes into further detail.
The above is not totally irrelevant to the original question. Having established that feeding the animals on the Ark was nowhere near so difficult as scoffers suppose, one immediate possible solution is that the Ark carried enough supplies to last for some time after. (Keep in mind that Noah et al were in the Ark for a little over a year; if, in that time, they used three quarters of their original supplies, the leftovers might still last for months.)
Another critical point is that most Creationists believe that no animals were created to be carnivorous. The ark was no opened until after a dove had brought back an olive branch, and subsequently left and not returned. This shows not only that plants were again growing, but suggests that the dove felt it could survive without relying on Noah to feed it. If we also suppose that the disembarking animals could still subsist, at least for a while, on a plant-based diet, we have substantially mitigated the food concerns. On top of that, one needs to bear in mind that aquatic animals were not wiped out.
The assumption that dozens of animals would immediately need to kill other land animals in order to survive is just that; an assumption. One should also keep in mind that it's hard to make a kill when there's perhaps only a hundred or so potential prey animals in the entire world.
On the other hand... the fossil record reveals any number of animals that are now extinct. While historic records of some of these persist until as recently as a few centuries ago, it may also be the case that some species were almost immediately killed off.