There are already a large number of solutions to Navier-Stokes that are known. The millennium problem asks to prove existence or non-existence of smooth (infin

There are already a large number of solutions to Navier-Stokes that are known. The millennium problem asks to prove existence or non-existence of smooth (infinitely differentiable) solutions that are valid for all time See pg 2, here: http://www.claymath.org/sites/default/files/navierstokes.pdf http://www.claymath.org/sites/default/files/navierstokes.pdf