On the essential spectrum of the linearized Navier-Stokes operator
type: Item
instance of: scholarly article
title: On the essential spectrum of the linearized Navier-Stokes operator
zbMATH Open document ID: 0970.35093
DOI: 10.1007/BF01192299
published in: Integral Equations and Operator Theory
publication date: 2001-10-10T00:00:00Z
review text: Let \(\Omega \) be a bounded domain in \(\mathbb{R}^n\), \(n \geq 2\), whose boundary is of class \(C^2\). Let \(H^p(\Omega)\) denote a Sobolev space. Let \(\mathbf L\) be the closure of the Stokes operator \[ \mathbf L_0 = \left( \begin{matrix} -\Delta I &-\text{grad}\cr \text{div} & 0 \end{matrix} \right), \] where \(I\) is the \(n \times n\) unit matrix, \(\mathbf L_0\) is defined on \(L^2(\Omega) ^n \times L^2(\Omega)\) with the image domain \((H^2(\Omega) \cap H^1_0(\Omega)) ^n \times H^1(\Omega)\). Then the essential spectrum of \(\mathbf L\) is \(( -1, -1/2) \).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35P05
Mathematics Subject Classification ID: 35G15
Mathematics Subject Classification ID: 35J45
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 1542579
zbMATH Keywords: matrix operator
zbMATH Keywords: essential spectrum
zbMATH Keywords: Stokes equations
author: M. Faierman
author: Rainer J. Fries
author: Reinhard Mennicken
author: Manfred Möller
reviewed by: Vladimir Mityushev
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01192299
OpenAlex ID: W2037890078
description: scientific article; zbMATH DE number 1542579