On two new inequalities for Leray solutions of the Navier-Stokes equations in \(\mathbb{R}^n\)
type: Item
instance of: scholarly article
title: On two new inequalities for Leray solutions of the Navier-Stokes equations in \(\mathbb{R}^n\)
zbMATH Open document ID: 1439.35369
author: Jens Lorenz
author: Paulo R. Zingano
author: Thomas Hagstrom
author: Janaína P. Zingano
published in: Journal of Mathematical Analysis and Applications
publication date: 2019-11-28T00:00:00Z
review text: 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.
reviewed by: Ahmed Lesfari
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 7138446
zbMATH Keywords: algebraic decay
zbMATH Keywords: exponential decay
zbMATH Keywords: Leray solutions
zbMATH Keywords: incompressible Navier-Stokes equations
zbMATH Keywords: Schonbek-Wiegner estimates
MaRDI profile type: Publication
full work available at URL: j.jmaa.2019.123601
OpenAlex ID: W2980345462
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DOI: 10.1016/J.JMAA.2019.123601
description: scientific article; zbMATH DE number 7138446