Laws of aerodynamics after breaking the sound barrier

my knowledge of physics is not very extensive, so I hope my question isn't too stupid.

I know that when (for instance) a plane breaks trough the sound barrier, the laws of the aerodynamics change.

But I don't know why because the plane is still being carried by the same air, only it's travelling much faster and this creates a state where the air is (in relation to the plane) much more dense. But I can't make out how this would have an effect on these aerodynamic laws.

-