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

TL;DR

This paper discusses a method for analyzing approximate solutions to the Euler and Navier-Stokes equations, providing bounds on their accuracy using a posteriori analysis in a smooth function framework.

Contribution

It introduces a variant of previous analysis that employs a C^infinity formulation to bound the Sobolev distance between exact and approximate solutions.

Findings

Provides a rigorous bound on the Sobolev distance

Extends previous analysis to a smooth function setting

Enhances understanding of solution accuracy in fluid dynamics

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.