The nonsteady Boussinesq system with mixed boundary conditions including conditions of friction type
type: Item
instance of: scholarly article
title: The nonsteady Boussinesq system with mixed boundary conditions including conditions of friction type
zbMATH Open document ID: 1465.76039
DOI: 10.1155/2020/6096531
author: Tujin Kim
published in: International Journal of Differential Equations
publication date: 2021-05-19T00:00:00Z
review text: Summary: In this paper, we are concerned with the nonsteady Boussinesq system under mixed boundary conditions. The boundary conditions for fluid may include Tresca slip, leak and one-sided leak conditions, velocity, static (or total) pressure, rotation, and stress (or total stress) together, and the boundary conditions for temperature may include Dirichlet, Neumann, and Robin conditions together. Relying on the relations among strain, rotation, normal derivative of velocity, and shape of the boundary surface, we get variational formulation. The formulations consist of a variational inequality for velocity due to the boundary conditions of friction type and a variational equation for temperature. For the case of boundary conditions including the static pressure and stress, we prove that if the data of the problem are small enough and compatibility conditions at the initial instance are satisfied, then there exists a unique solution on the given interval. For the case of boundary conditions including the total pressure and total stress, we prove the existence of a solution without restriction on the data and parameters of the problem.
Mathematics Subject Classification ID: 76E06
Mathematics Subject Classification ID: 76M30
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 80A19
zbMATH DE Number: 7349533
zbMATH Keywords: variational inequality
zbMATH Keywords: free convection
zbMATH Keywords: heat transfer
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
Wikidata QID: Q115243812
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/6096531
OpenAlex ID: W3083374463
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description: scientific article; zbMATH DE number 7349533