Let us suppose that there exists a (initially smooth) solution of NSE that blows up in finite time. Then, in particular, the corresponding velocity field becomes unbounded as time progresses. Which assumptions in the common modelling of fluid flow (leading to NSE) will be violated and in which way will NSE need to be adjusted?

I read that the viscous term is some kind of expansion and higher derivatives of the velocity field u, like \Delta^2 u, should, in fact, be retained. (It´s well-known that NSE with hyperdissipation admits global smooth solutions.) Unfortunately, i couldn't find any physical details on this expansion. Does someone know about it? Thanks a lot in advance! :-)