On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations
type: Item
instance of: scholarly article
title: On a bilinear estimate in weak-Morrey spaces and uniqueness for Navier-Stokes equations
zbMATH Open document ID: 1334.35204
published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série
publication date: 2015-12-28T00:00:00Z
review text: The Navier-Stokes equations are studied, where the bilinear term \(B(u,u)\) is given in terms of the heat semigroup and Leray projector -- see formula (5.1). The main point is to give a new estimate of \(B(u,u)\) in the functional space \(L^{\infty}((0,T);X)\), where \(X\) is a Morrey space. The Morrey spaces are used in order to improve the Sobolev embedding theorem -- see the useful paper [\textit{M. Rupflin}, ``What is a\dots Morrey space? What is a\dots Campanato space?''], available on Google. The new estimate of \(B(u,u)\) is obtained by using the Lorentz spaces (see Section 2.1) and block spaces (see Section 3.1). The block spaces are defined in terms of Lorentz spaces and contain a weight \(\rho\). On this way, the author can avoid the Besov spaces. It is proved that the block space is the predual of the Morrey space. The estimate of the bilinear term is obtained by using Holder type inequalities, some estimates of the heat semigroup on the block spaces, interpolation of operators and duality.
reviewed by: Gelu Paşa
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35A02
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 6524293
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: bilinear term estimates
zbMATH Keywords: Morrey spaces
author: Lucas C. F. Ferreira
MaRDI profile type: Publication
full work available at URL: j.matpur.2015.10.004
OpenAlex ID: W2175721338
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DOI: 10.1016/J.MATPUR.2015.10.004
description: scientific article; zbMATH DE number 6524293