On a free boundary problem for the stationary Navier-Stokes equations
type: Item
instance of: scholarly article
title: On a free boundary problem for the stationary Navier-Stokes equations
zbMATH Open document ID: 0637.76027
DOI: 10.1016/S0294-1449(16)30355-9
author: Josef Bemelmans
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78142
review text: [See also the author's article reviewed above (Zbl 0637.76026).] We investigate stationary flows in a fluid body together with its free boundary. The fluid is assumed to be viscous and incompressible; the free boundary is governed by continuity of the normal stress. Hence the configuration to be considered here can be regarded as a generalization of a classical equilibrium figure. The main tool in proving existence of a regular solution consists in a hard implicit function theorem.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 4039460
zbMATH Keywords: stationary flows
zbMATH Keywords: free boundary
zbMATH Keywords: classical equilibrium figure
zbMATH Keywords: existence of a regular solution
zbMATH Keywords: implicit function theorem
MaRDI profile type: Publication
cites work: Gleichgewichtsfiguren zäher Flüssigkeiten mit Oberflächenspannung
cites work: Liquid drops in a viscous fluid under the influence of gravity and surface tension
cites work: The boundary problems of physical geodesy
cites work: Locally coercive nonlinear equations, with applications to some periodic solutions
cites work: Q4477944
cites work: Q5520417
cites work: The imbedding problem for Riemannian manifolds
cites work: A rapid convergence method for a singular perturbation problem
cites work: SOLVABILITY OF A PROBLEM ON THE MOTION OF A VISCOUS INCOMPRESSIBLE FLUID BOUNDED BY A FREE SURFACE
cites work: On a boundary value problem for a stationary system of Navier-Stokes equations
cites work: Q5607484
cites work: Q5681180
cites work: Generalized implicit function theorems with applications to some small divisor problems, I
description: scientific article; zbMATH DE number 4039460