It depends on what type of corks you are using. If you are using a synthetic cork, it is not "neccessary" to lie them down on their sides, but you still run a chance of them drying out over an extended period. If you are using a natural cork, you should keep it on it's side to prevent drying out. Another thing you can do is just stand them up, upside down so the cork is still touching the wine. Just remember to bring it right side up for a few hours before serving to bring the sediment back to the bottom.
I would highly recommend going with natural corks if you are planning on aging this wine though. The natural corks allow good oxygen contact through the pourous material which allows for good aging. Again, only if stored on it's side though. Hope this helps!