My understanding is that the Navier-Stokes problem has to do with showing that smooth solutions always exist for the three dimensional system of equations, so a

My understanding is that the Navier-Stokes problem has to do with showing that smooth solutions always exist for the three dimensional system of equations, so a counter-example would be a set of initial conditions for which no smooth solution exists. On Wikipedia, the problem is described as: "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." http://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smoothness http://en.wikipedia.org/wiki/Navier–Stokes_existence_and_smo...