Stationary solutions of the heat convection equations in exterior domains
type: Item
instance of: scholarly article
title: Stationary solutions of the heat convection equations in exterior domains
zbMATH Open document ID: 0894.35041
author: Kazuo Ōeda
published in: Proceedings of the Japan Academy. Series A
publication date: 1998-04-20T00:00:00Z
review text: Let \(\Omega= K^c\subset\mathbb{R}^3\), where \(K\) is a compact set whose boundary \(\partial K\) is of class \(C^2\). We put \(\partial\Omega= \Gamma= \partial K\). Then we consider the stationary problem for the heat convection equation (HCE) in \(\Omega\): \[ (u\cdot\nabla)u= -(\nabla p)/\varrho+ \{1-\alpha(\theta- \Theta_0)\}g+ \nu\Delta u\quad\text{in }\Omega, \] \[ \text{div }u= 0,\quad (u\cdot\nabla)\theta= \kappa\Delta\theta\quad\text{in }\Omega, \] \[ u|_\Gamma= 0,\quad \theta|_\Gamma= \Theta_0>0,\quad \lim_{| x|\to\infty} u(x)= 0,\quad \lim_{| x|\to\infty} \theta(x)= 0. \] The purpose of the present paper is to show the existence of stationary weak solutions of (HCE) by using the ``the extending domain method''. Moreover, we also study the uniqueness of a weak solution.
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35J55
Mathematics Subject Classification ID: 80A20
zbMATH DE Number: 1143821
zbMATH Keywords: existence
zbMATH Keywords: extending domain method
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: pjaa.73.111
OpenAlex ID: W2169914211
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DOI: 10.3792/PJAA.73.111
description: scientific article; zbMATH DE number 1143821