Oseen resolvent estimates with small resolvent parameter
type: Item
instance of: scholarly article
title: Oseen resolvent estimates with small resolvent parameter
zbMATH Open document ID: 1394.35319
author: Paul Deuring
published in: Journal of Differential Equations
publication date: 2018-04-16T00:00:00Z
review text: The Oseen resolvent system in 3D exterior domain is studied in the paper. \[ -\Delta u+\tau\frac{\partial u}{\partial x_1}+\lambda u+\nabla \pi=f,\quad \text{div}\,u=0,\quad x\in\Omega, \] \[ u=0\quad \text{on}\;\partial\Omega, \] where \(\Omega\) is an open set in \(\mathbb{R}^3\) with bounded complement, \(\tau\) is a positive constant corresponding to Reynolds number, \(f\) is a given vector function, vector \(u\) and scalar \(\pi\) are unknown functions, \(\lambda\in\mathbb{C}\) is a spectral parameter. The series of estimates for the function \(u\) are obtained for \[ \lambda\in\mathbb{C}\setminus\{0\},\quad \text{Re}\,\lambda\geq 0,\quad |\lambda|\leq\frac{\tau^2}{4}. \] It is proved in particular that \[ \| u \|_p\leq\frac{C}{\lambda^2}\| f \|_p \] for any \(p>1\). The application of results of the article are discussed.
reviewed by: Il'ya Sh. Mogilevskii
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35P99
Mathematics Subject Classification ID: 76D07
zbMATH DE Number: 6860139
zbMATH Keywords: Stokes system
zbMATH Keywords: Oseen spectral problem
zbMATH Keywords: resolvent estimates
MaRDI profile type: Publication
full work available at URL: j.jde.2018.02.033
OpenAlex ID: W2796433282
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Wikidata QID: Q130017812
DOI: 10.1016/J.JDE.2018.02.033
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description: scientific article; zbMATH DE number 6860139