My house has a similar issue with a lower level that is perpetually much colder than the upper level. The main way we have somewhat alleviated the problem is by opening/closing registers. In the summer, we close all the registers in the lower level, forcing all the cold air from the HVAC into the upper level, then letting it sink down naturally. Our lower level is still cooler, but it isn't as stark a difference. Due to the layout of the stairs linking the two levels, a fan is not terribly effective at exchanging a lot of air between the two on its own.