A long time ago, I started working on an approach that never panned out, attempting to prove that such solutions could not exist. I will briefly mention it her

A long time ago, I started working on an approach that never panned out, attempting to prove that such solutions could not exist. I will briefly mention it here in case anyone would like to comment or continue the strategy. In [1] I learned that it is known that certain differential equations associated with embedding manifolds in R^n possess no smooth solutions. And in [2] I asked if it was possible that the Navier-Stokes equations were of this nature, since if this was the case it would create a clear path towards a negative solution. There was no definitive answer given, but the community (of mathSE) did seem to agree that it would turn it this is not the case. [1] http://math.stackexchange.com/questions/8586/what-is-an-example-of-a-second-order-differential-equation-for-which-it-is-known http://math.stackexchange.com/questions/8586/what-is-an-exam... (See Willie Wong's answer) [2] http://math.stackexchange.com/questions/9085/manifold-interpretation-of-navier-stokes-equations http://math.stackexchange.com/questions/9085/manifold-interp...