Weak continuity in convection problems
type: Item
instance of: scholarly article
title: Weak continuity in convection problems
zbMATH Open document ID: 0621.76102
DOI: 10.1016/0022-247X(85)90335-X
author: Dan Polisevski
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: The Darcy-Boussinesq system of equations, which governs the steady natural convection in fluid-saturated porous media, is studied. The existence of the weak solutions is proved by a slight generalization of \textit{J. P. Gossez}'s theorem [Acad. Roy. Belgique, Bull. Cl. Sci., V. Sér. 52, 1073-1077 (1966; Zbl 0148.387)]. A maximum principle is obtained by the technique of inequalities in Sobolev spaces. Further regularity properties and an uniqueness criterion (in terms of the dimensionless Rayleigh number) are presented.
Mathematics Subject Classification ID: 76S05
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 4008014
zbMATH Keywords: weak continuity
zbMATH Keywords: coercive operator
zbMATH Keywords: weak solution
zbMATH Keywords: Darcy-Boussinesq system of equations
zbMATH Keywords: steady natural convection
zbMATH Keywords: fluid-saturated porous media
zbMATH Keywords: maximum principle
zbMATH Keywords: inequalities
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: regularity properties
zbMATH Keywords: uniqueness criterion
MaRDI profile type: Publication
cites work: On thermal equation for flow in porous media
cites work: Q5527426
cites work: Structure of the set of stationary solutions of the navier‐stokes equations
cites work: Q4053162
cites work: Q4040640
full work available at URL: 0022-247x(85)90335-x
OpenAlex ID: W1977683836
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description: scientific article; zbMATH DE number 4008014