Can I sleep in an airport?

This semester I need to visit someone every month or so and I have cl Monday and Wednesday (7 PM) each week, so I have from basically Wed. night to travel there, and Sunday evening to travel back. This could work except the only way I can see it happening is if I sleep in the airport... because the train arrives at the airport at 11:30 and the first flight out is 6 AM, so that's almost 7 hours in the airport in which I could sleep... it would be hard to get a room but I'm just checking my options for now. Thanks!