Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus
type: Item
instance of: scholarly article
title: Reduced and generalized Stokes resolvent equations in asymptotically flat layers. II: \(H_\infty\)-calculus
zbMATH Open document ID: 1083.35085
author: Helmut Abels
published in: Journal of Mathematical Fluid Mechanics
publication date: 2005-06-16T00:00:00Z
review text: The author studies the generalized Stokes resolvent equations and proves that they are uniquely solvable if and only if a suitable system of reduced Stokes equations are uniquely solvable. The reduced system fits well into the general calculus of parameter-dependent pseudodifferential boundary value problems developed by Grubb in 1966. The calculus here developed is used to construct a parametrix to the reduced Stokes system, which coincides with the exact solution operator modulo term which decay faster as \(|\lambda|\to\infty\). Using this parametrix it is proved that the usual Stokes operator in the Dirichlet case and the reduced Stokes operator in the mixed case admit a bounded \(H_\infty\)-calculus in the sense of McIntosh. A nonsmooth version of parameter dependent Green operators is considered, too.
reviewed by: Silvio Nocilla
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35S15
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35A17
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 2176391
zbMATH Keywords: Stokes equations
zbMATH Keywords: free boundary value problems
zbMATH Keywords: non-smooth pseudodifferential operators
MaRDI profile type: Publication
full work available at URL: s00021-004-0117-7
OpenAlex ID: W1976713293
DOI: 10.1007/S00021-004-0117-7
description: scientific article; zbMATH DE number 2176391