On the integral representation of the solution to the Stokes system
type: Item
instance of: scholarly article
title: On the integral representation of the solution to the Stokes system
zbMATH Open document ID: 0593.35066
author: Alberto Valli
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1985-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108013
review text: The paper is a synthetic and critical analysis of the linearized Navier- Stokes system: \(\Delta v-\nabla p=f\), div v\(=g\), \(v|_{\partial \Omega}=\phi\). The method used by the author is the Green's one, by means of which he expresses the pressure and the velocity field in terms of \(\Omega\), f, g, \(\phi\). Theorems of existence and uniqueness are also proved. What is very interesting in the paper is its critical aspect, which put in discussion the very ancient results obtained by famous specialists in the viscous flow problems. The author finds some results of F. K. G. Odqvist, H. Villat, O. A. Ladyzhenskaya and other ones as incorrect, incomplete or not well-grounded. His unexpected remarks are very useful for all interested in the domain.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35C15
zbMATH DE Number: 3953389
zbMATH Keywords: slow viscous
zbMATH Keywords: Green's method
zbMATH Keywords: integral representation of solution
zbMATH Keywords: linearized Navier-Stokes system
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3953389