Stationary Stokes and Navier-Stokes systems in an infinite open channel. II
type: Item
instance of: scholarly article
title: Stationary Stokes and Navier-Stokes systems in an infinite open channel. II
zbMATH Open document ID: 0714.35067
DOI: 10.1007/BF00966078
published in: Lithuanian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: [For Part I, see Lith. Math. J. 29, No. 1, 34--47 (1989); translation from Litov. Mat. Sb. 29, No. 1, 90--108 (1989; Zbl 0703.35149).] In part I the main problems were formulated. Existence and uniqueness theorems are proved for solutions of certain boundary problems related with the stationary Stokes equations, giving a priori estimates in appropriate weighted Sobolev norms, and weighted Hölder norms also. Existence theorems are obtained for generalized solutions of boundary problems related with the stationary Navier-Stokes equations. An adequate representation (according the asymptotics as \(| x| \to \infty)\) of the solution, its uniqueness and a priori estimates in different functional spaces, are given under certain conditions.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B45
zbMATH DE Number: 4175583
zbMATH Keywords: Existence
zbMATH Keywords: uniqueness
zbMATH Keywords: Stokes equations
zbMATH Keywords: weighted Sobolev norms
zbMATH Keywords: weighted Hölder norms
author: K. Pileckas
author: V. A. Solonnikov
reviewed by: Mariano Rodríguez Ricard
MaRDI profile type: Publication
cites work: Solvability of three-dimensional problems with a free boundary for a stationary system of Navier-Stokes equations
cites work: Some problems of vector analysis and generalized formulations of boundary-value problems for the Navier-Stokes equations
cites work: [Russian Text Ignored]
full work available at URL: https://doi.org/10.1007/bf00966078
OpenAlex ID: W2090151085
Recommended article: Stationary Stokes and Navier-Stokes systems in an infinite open channel. I
Recommended article: Q4551588
Recommended article: Q4471257
Recommended article: Q5479931
Recommended article: The relation between stationary and periodic solutions of the Navier-Stokes equations in two or three dimensional channels
Recommended article: Q5188485
Recommended article: Solutions of the stationary Navier-Stokes system of equations with an infinite Dirichlet integral
Recommended article: A remark on the existence of steady Navier-Stokes flows in a certain two-dimensional infinite channel.
Recommended article: A stability result for the Stokes-Boussinesq equations in infinite 3D channels
Recommended article: On the structure of stationary solutions of the Navier-Stokes equations
description: scientific article; zbMATH DE number 4175583