You are liable for the tickets. If you don't pay them, or go to court on the date and time stipulated on the ticket, then the court will do a check on the owner of the vehicle and when you get stopped again you will find a bench warrant waiting for you.
if you have any evidence you can mail it in with not guilty pleas, you won't have to go in person to fight a parking ticket. i've gotten 1 cut in half, and the other i spending, i took photos and sent them in with a written statement as evidence
good luck, and read those parking signs carefully when in ny