I would think it very likely that, IF the earth is flat, the governments of most (maybe all) the countries, and the industries, would be intent on exploring the Edge, the Barrier, the Dropping-Off Line, whatever you wanna call it. Because beyond that point, over the side or wherever, there may be new resources - petroleum or gold or something we aren't even familiar with, and maybe entirely new life forms ... maybe even sentient beings, maybe land open for population and cultivation.
If the earth is, as the vast majority of educated people think, round, then scientists are interested in more studies of climate and meteorology, earth sciences, and the like, as well as the details of the physics of space travel to the moon and the nearest planets, and studies of cosmic radiation and solar energy and flares.