“Well, hang in there.”

You're talking on the phone with your sister, who's in medical school. She tells you about how hard her classes are and the number of hours she has to spend studying. You want to say something to encourage her. You say:

Well, hang in there.

well,

This is used to start a sentence when you're changing the topic. In the case above, the topic is still your sister's medical school, but you're changing from her describing her situation to you giving her advice or encouragement.

hang in there

"Hang in there" means "don't give up." This is specifically used when someone is in a difficult or stressful situation. You say this to encourage them.

This phrase is a little casual but can be used in most situations where you're speaking one-on-one with someone.