From Longman Dictionary of Contemporary Englishstay up phrasal verbto not go to bed at the time you would normally go to bedWe stayed up all night talking.I let the kids stay up late on Fridays. →stay→ See Verb table
Examples from the Corpus
stay up• Kate stayed up all night by his bedside.• You guys go ahead and go to bed. I think I'll stay up for a while.• That night Carl stayed up into the small hours, preparing work for the next day.• Didn't you even stay up on election night?• We went to bed, but Julie and Kate stayed uptalking and playing cards.stay up late• She stays up late at night painting.• And I thought the newsroompizza was the only reason to stay up late election night.• It was downright ridiculous, if you ask anyone who stayed up late enough to watch the end.• The night before the trip, we sisters stayed up latepacking and gabbing.• Anne began acting worse-was rebellious, stayed up late, slept in the daytime.• I stayed up late to clear things up, and got up early to do the same thing.• Marguerite stayed up late watching the testpattern.• The Huskies would be advised to stay up late working on showing up early.