Comment by krackers

At the time that the Millenium Prize problems were formulated, the force term was understood to make the problem more realistic, since real fluids are always going to have external forces applied to them. A blowup that happens under constant gravity, for example, would probably be no less interesting than an entirely unforced blowup. The strategy of constructing impossibly complex external forces to induce a blowup was pioneered by Córdoba and Martínez-Zoroa only over the past few years.