An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions.
type: Item
instance of: scholarly article
title: An existence theorem for the Boussinesq equations with non-Dirichlet boundary conditions.
zbMATH Open document ID: 1067.35080
DOI: 10.1023/A:1022224328555
author: Zdeněk Skalák
author: Petr Kučera
published in: Applications of Mathematics
publication date: 2000-09-14T00:00:00Z
review text: The classical Navier-Stokes system for incompressible fluid in a bounded domain \(\Omega \subset \mathbb R^ 3\) is coupled with heat equation to render thermal effects (Boussinesq approximation). The boundary \(\partial\Omega\) is split into 5 subsets \(\Gamma_j,\) where the Dirichlet boundary condition for velocity is given on \(\Gamma_1,\) normal component of stress tensor on \(\Gamma_2\) and Dirichlet, Neumann and Newton boundary condition on \(\Gamma_3, \Gamma_4\) and \(\Gamma_5,\) respectively. Initial data for velocity and temperature are prescribed. For given problem the existence and uniqueness of local (maximal) weak solution is proved by an application Schauder fixed point principle.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 1508451
zbMATH Keywords: Boussinesq equations
zbMATH Keywords: non-Dirichlet boundary conditions
zbMATH Keywords: Sobolev space with non-integer order derivatives
zbMATH Keywords: Schauder principle
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1508451