New approach to the Hadamard variational formula for the Green function of the Stokes equations
type: Item
instance of: scholarly article
title: New approach to the Hadamard variational formula for the Green function of the Stokes equations
zbMATH Open document ID: 1312.35142
author: Erika Ushikoshi
published in: Manuscripta Mathematica
publication date: 2015-01-19T00:00:00Z
review text: The Stokes equations are considered in a two-dimensional bounded domain \(D\). The solution is obtained by using the Green's functions \(G,R\) for velocity and pressure. The variation of \(G,R\) is studied, when \(D\) is perturbed with a preserving volume (and topological type) transformation. The new element is a formula for higher derivatives of \(G,R\) in terms of the domain perturbations, obtained by using also some previous results of the author. The main tools are a Schauder type estimate and some relations concerning the fundamental stress tensor on the surface integrals.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 6387829
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: s00229-014-0695-5
OpenAlex ID: W2032529767
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DOI: 10.1007/S00229-014-0695-5
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description: scientific article; zbMATH DE number 6387829