On two new inequalities for Leray solutions of the Navier-Stokes equations in \(\mathbb{R}^n\)
The aim of this note is to derive two new inequalities for arbitrary Leray solutions of the incompressible Navier-Stokes equations (in dimension \(2\leq n\leq4\)). These two asymptotic inequalities, not observed previously, are valid for arbitrary spatial derivatives of Leray solutions to incompressible Navier-Stokes equations in \(\mathbb{R}^n\), \(n\leq4\). In addition, they are important for studying the disintegration of solution derivatives. This note is organized as follows: the first section is an introduction to the subject. In the second section, the authors recall some basic material that will be needed in the derivation of some inequalities in the next sections. The third and fourth sections, which contain the main results of this note, deal with some technical statements which will serve in the proof of two fundamental inequalities.
scientific article; zbMATH DE number 7138446
scientific article