follow something up 
phrasal verb with follow verb uk/ˈfɒl.əʊ/ us/ˈfɑː.loʊ/
  (US also follow up on something)      
B2 追查…的更多情况;对…采取进一步行动
to find out more about something, or take more action connected with it
  The idea sounded interesting and I decided to follow it up. 这个想法听起来很有趣,我决定要作进一步的了解。 
 He decided to follow up on his initial research and write a book. 他决定继续进行他最初的研究,然后写本书。