Yes div(v)=0 is assumed.
Its obvious since water gushes out of a pipe faster when you partially cover the opening.
Its because whatever volume flowing into pipe per unit time=water flowing out of pipe per unit time.
Theoretically speaking it would be possible to store light since the ponting vector has a non zero divergence.Which means that whatever power in form of electromagnetic fields flows into a closed surface,the same amount of power may not necessarily flow out of the surface.So there can be a net...