Smooth solutions of the Euler and Navier-Stokes equations from the a posteriori analysis of approximate solutions
arXiv:1405.3421 · doi:10.1016/j.na.2014.10.005
Abstract
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.
Author's note. Some overlaps with our previous works arXiv:1402.0487, arXiv:1310.5642, arXiv:1304.2972, arXiv:1203.6865, arXiv:1104.3832, arXiv:1009.2051, arXiv:1007.4412, arXiv:0909.3707, arXiv:0709.1670; these overlaps aim to make the paper self-contained and do not involve the main results. Final version to appear in Nonlinear Analysis