Two Story Family Room Stays Cold in Winter; Open 2nd Story Hallway Very Warm

I live in a two story home with a living room on the main level that has a 2-story ceiling. We have a lot of trouble keeping the main level warm in the winter as most of the heat escapes upstairs because of the open hallway on the second level. We use a ceiling fan in the living room, but it still gets too warm upstairs and the temp on the main level is too cool. Plus, the ceiling fan blowing on us is very annoying. I've had the ceiling fan blowing in both clockwise and counter-clockwise directions, but the result is the same either way. It seems like the open hallway on the second level is the problem, but without building a wall, is there anything I can do??? I will post photos soon.

Thanks,
Kyle

 

Here is a view from my main level living room up to the ceiling and open stairway.

 

Where are your supply & return registers & grills located? If the supplys come out of the ceiling, there's your problem.