what can one do in case of an abuse?

I would ask him/her why she do not want to report it. There are many reasons to why the person do not want to report it. He/she might be afraid to see the abuser again and it is frightening to say these things again and again (to police and the court). Not many have the courage to do it as it can be emotionally draining to go through the whole process. What I think is that what you can do is try to be supportive towards him/her, no matter what decision the person has made.

Abuse is a terrible thing to experience and it can leave you scarred for life. I would definitely speak up if it was happening to me and if it were a friend I would speak up for their sake too

sometimes there are good reasons why a victim refuse to report the abuse, perhaps she is protecting someone - like her family or someone close to her that will be affected directly if she told the truth, or perhaps she is afraid, maybe the suspect has threatened her to keep her mouth shut or else something bad will happen to her or her family. Sometimes a victim shut her mouth for a simple reason that she is ashamed of the scandal that might happen if she file a complaint. perhaps what you can do is to convince her to confess before you make any move of reporting the incident, in that way you will have a chance to make her talk and finally admit what really had happen.