Prove or give a counter-example of the following statement:

In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the Navier–Stokes equations.

More info:

https://en.m.wikipedia.org/wiki/Navier%E2%80%93Stokes_existence_and_smoothness

This market resolves to YES if the Clay Mathematics Institute (or equivalent organization) agrees that the Navier-Stokes problem has been solved

Otherwise this market resolves to NO.