Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity
type: Item
instance of: scholarly article
title: Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity
zbMATH Open document ID: 0891.35117
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1998-07-19T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108426
review text: The solvability of the stationary Navier-Stokes equations in weighted Sobolev and Hölder spaces is studied. The class of domains \(\Omega\subset\mathbb{R}^n\), \(n= 2,3\), having \(m>1\) exits to infinity \(\Omega_i\) of the form \[ \Omega_i= \{x\in\mathbb{R}^n;\;|x'|< g_i(x_n),\;x_n>0\} \] and the flow of viscous incompressible fluid in such domain is considered. First, the problem in the case of zero fluxes in the space of exponentially vanishing at infinity functions is studied. These results are based on the Banach contraction principle and refer to dimensions \(n=2,3\). Then, for arbitrarily fluxes and in three-dimensional domains \(\Omega\) the solvability of this problem for arbitrarily large data is proved. The case of two-dimensional domains \(\Omega\) is more complicated and for such domains the solvability only for small data is proved.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 35A05
zbMATH DE Number: 1089780
zbMATH Keywords: Navier-Stokes equations
zbMATH Keywords: solvability
zbMATH Keywords: domains with exits to infinity
author: K. Pileckas
reviewed by: A. Cichocka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1089780