Smooth solutions of the Euler and Navier-Stokes equations from the a   posteriori analysis of approximate solutions
  The main result of [C. Morosi and L. Pizzocchero, Nonlinear Analysis, 2012] is presented in a variant, based on a C^infinity formulation of the Cauchy problem; in this approach, the a posteriori analysis of an approximate solution gives a bound on the Sobolev distance of any order between the exact and the approximate solution. 
Carlo Morosi (Politecnico di Milano), Livio Pizzocchero (Universita'   di Milano)
math.AP