Some victims do not report abuse and violence they are suffering. discuss two reasons why many cases of abuse and violence are not repported

 The fear of not being believed , if there are no witnesses , is a major reason in the case of sexual assault. 
Together with a feeling of shame and/or fear of reprisal by the offender. 

Defence of such charges (against adult victims) usually argues the sexual encounter was consensual, or seeks to prove the victim is someone of loose morals and/or went further than intended - or the charge is totally false/malicious. 

It's often difficult to prove 'guilt beyond all reasonable doubt' and many victims simply prefer to avoid the publicity and possible denigration of their character. 

As regards domestic violence - the young will often be under threat of even more violence if they report the abuse - as can apply to adults, particularly females who might actually still 'love' the perpetrator, despite the violence - which will often result from a drink or drug problem, the bully expressing 'remorse' and promise not to do it again. 
Until the next time, etc.