On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on \(L^{\infty }\)
type: Item
instance of: scholarly article
title: On heat convection equations in a half space with non-decaying data and Stokes semi-group on Besov spaces based on \(L^{\infty }\)
zbMATH Open document ID: 1171.35100
author: Yasushi Taniuchi
published in: Journal of Differential Equations
publication date: 2009-04-29T00:00:00Z
review text: The authors study the Boussinesq model of a viscous incompressible fluid in the \(n+1\) dimensional half space, \[ \mathbb R^{n + 1}_{+} = \{x= (\tilde{x},x_n)\in \mathbb R^{n + 1}; \tilde{x} \in \mathbb R^{n}, x_{n + 1} > 0\}. \] The local existence theorem for the Boussinesq equations with non-decaying data is established in the Besov space \(\mathbf B^\alpha_{pq}\) with the help of the continuity equation and the Dirichlet boundary conditions. The Besov space \(\mathbf B^\alpha_{pq}\) is a complete quasinormed space which is a Banach space when \(1 \leq p, q \leq \infty\). Finally, the uniqueness of the problem is proved.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 5549447
zbMATH Keywords: Stokes semi-group
zbMATH Keywords: viscous incompressible fluid
zbMATH Keywords: Boussinesq equation
zbMATH Keywords: Besov space of negative order
MaRDI profile type: Publication
full work available at URL: j.jde.2009.01.011
OpenAlex ID: W2080825405
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DOI: 10.1016/J.JDE.2009.01.011
description: scientific article; zbMATH DE number 5549447