Weak solutions of Navier-Stokes equations constructed by artificial compressibility method are suitable

TL;DR

This paper proves that weak solutions of the Navier-Stokes equations, constructed via the artificial compressibility method, are suitable in the sense of Scheffer, using advanced mathematical techniques for estimates and limits.

Contribution

It establishes the suitability of weak solutions obtained through the artificial compressibility method, a significant step in understanding their mathematical properties.

Findings

Weak solutions are suitable in the sense of Scheffer.

Nontrivial estimates of pressure and time derivatives are obtained.

The limit passage is justified using Fourier transform techniques.

Abstract

In this paper we prove that weak solution constructed by artificial compressibility method are suitable in the sense of Scheffer. Using Hilbertian setting and Fourier transform with respect to the time we obtain nontrivial estimates of the pressure and the time derivate which allow us to pass into the limit.