There are contingencies for radio outages, but yeah, everything going down at once (if that's what's happening here, which I doubt) is bad.
I would hope that airports keep a battery operated radio + antenna in case of emergency with them, to at least communicate with aircraft within visual range of the airport.
So it falls back to local control, more in the style of visual flight rules. Pilots in existing flights will have to be vigilant and do their own deconflictation and stop new flights out until the network is back up.
All conjecture at this stage of course, but all the radios won't just fail. It is probably going to be a poster child example about the dangers of large scale integration. The attraction of course is that integration is very efficient, the danger is it tend to fail all at once instead of in smaller pieces.