The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure.
type: Item
instance of: scholarly article
title: The boundary regularity of a weak solution of the Navier-Stokes equation and its connection to the interior regularity of pressure.
zbMATH Open document ID: 1099.35087
DOI: 10.1023/B:APOM.0000024493.04008.06
author: Jiří Neustupa
published in: Applications of Mathematics
publication date: 2006-11-21T00:00:00Z
full work available at URL: https://eudml.org/doc/33167
review text: In this paper the author deals with a weak solution \({\mathbf v}\) to the non-steady Navier-Stokes equations in a bounded domain \(\Omega \) that satisfies the strong energy inequality. The author assumes that conditions of the Prodi-Serrin type are satisfied in a certain neighbourhood of the boundary. He shows the consequence for the regularity of \({\mathbf v}\) near the boundary and the connection with the interior regularity of an associated pressure and the time derivative of \({\mathbf v}\). In order to prove this results the author uses fine properties of the Stokes operator A, which is selfadjoint and positive in \(L^2_{\sigma }(\Omega )^3\).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 5074706
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: conditions of Prodi-Serrin type
MaRDI profile type: Publication
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OpenAlex ID: W1969710486
description: scientific article; zbMATH DE number 5074706