curl up

US /kɜːrl ˈʌp/
UK /kɜːrl ˈʌp/
"curl up" picture
1.

to sit or lie in a position with your arms and legs close to your body

:
She likes to curl up on the sofa with a good book.
The cat curled up in a ball on the rug.
2.

if something such as paper or a leaf curls up, its edges bend inwards

:
The old photographs had started to curl up at the edges.
The heat made the leaves curl up and turn brown.