Smooth solutions of the Euler and Navier–Stokes equations from the a posteriori analysis of approximate solutions

The main result of Morosi and Pizzocchero (2012) is presented in a variant, based on a C∞C∞ 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.