I'm currently a PhD student in a field which heavily uses the Navier-Stokes equations. I have had for some time a question regarding the Clay Mathematics Institute 'Existence and Smoothness of the Navier-Stokes Equations'.
I have seen that the common interpretation of the stated problem is that to solve the problem one must obtain a full analytical solution of the N-S equations to describe all 3D, Newtonian, incompressible flows. However, from my own knowledge and reading how the problem is stated by the Clay institute, I believe that is not necessary. The problem simply requires someone shows that the N-S equations always yield solutions that exist and are smooth, regardless of initial conditions. To accomplish this one may derive an analytical solution, but it is not necessary to prove existence and smoothness.
Is my interpretation of the Clay institute problem correct? Or is an analytical solution of the N-S equations actually required to guarantee existence and smoothness of the solutions and solve the problem.