One of two things will happen at this point
1) He will go over the cliff and fire a missile, which will cause his entire country to be decimated in hours.
2) He'll back off and we'll send him a shitload of money like we always have with his dad to keep him quiet for a few more years.
There is another possibility, that if #2 happens a military coupe could take place as he might be seen as weak to his commanders, and I'm unsure of just how successful that would be, it would really depend on how many hard line loyalists he has within his inner circle. This could then lead to #1 happening at a future point if the coupe was successful, but this is an unlikely scenario.
I'm guessing he'll eventually shut up and we'll send him a few hundred million to be quite for a while.