Sharp existence results for the stationary Navier-Stokes problem in three-dimensional exterior domains
type: Item
instance of: scholarly article
title: Sharp existence results for the stationary Navier-Stokes problem in three-dimensional exterior domains
zbMATH Open document ID: 0965.35111
author: P. J. Rabier
author: Giovanni Paolo Galdi
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-07-19T00:00:00Z
review text: The stationary Navier-Stokes system is considered in an exterior domain \(\Omega\subset \mathbb{R}^3\) \[ \begin{aligned} -&\Delta v+\lambda v\cdot\nabla v+\nabla p=f,\quad \nabla\cdot v=0 \quad \text{in \;} \Omega,\\&v=v_0 \quad \text{on \;}\partial \Omega,\quad \lim_{|x|\to\infty}v(x)= v_{\infty}.\end{aligned} \] The authors investigate this problem in specific Sobolev-like spaces. Using the theory of Fredholm operators and topological degree arguments they establish the existence of solutions and the finiteness of the number of solutions for fixed \(v_0\) and generic \(f\). In particular the existence is obtained for an arbitrary \(f\in L^{\frac 43}(\Omega)\).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 76D05
zbMATH DE Number: 1538595
zbMATH Keywords: stationary Navier-Stokes equations
zbMATH Keywords: exterior domain
zbMATH Keywords: Fredholm operator
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: s002050000104
OpenAlex ID: W2094324125
DOI: 10.1007/S002050000104
description: scientific article; zbMATH DE number 1538595