“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 say this to encourage her.
Well, hang in there.
You use "well" to change the topic or the tone of a conversation:
A: How are your classes going?
B: Not too well, to be honest. Calculus is kicking my butt.
B: Yeah, I'll try. Hey, have you talked to Priscilla lately?
You can also use "well" to signal the end of a conversation. For example, you might say this after talking to someone who's just returned to work from maternity leave:
"Hang in there" means "don't give up." Specifically, we use "hang in there" when someone is in a difficult or stressful situation. You say this to encourage them:
A: This job is really hard. I don't know if I can do it.
B: Hang in there. You'll get used to it eventually.
"Hang in there" is a little casual but it's fine to use in most situations.