The Stokes operator in weighted \(L^q\)-spaces. I: Weighted estimates for the Stokes resolvent problem in a half space
type: Item
instance of: scholarly article
title: The Stokes operator in weighted \(L^q\)-spaces. I: Weighted estimates for the Stokes resolvent problem in a half space
zbMATH Open document ID: 1040.35060
author: Andreas Fröhlich
published in: Journal of Mathematical Fluid Mechanics
publication date: 2003-08-27T00:00:00Z
review text: The Stokes resolvent problem \[ \lambda v-\Delta v+\nabla p=f, \quad \text{div\,} v=g \quad \text{in \;} \mathbb{R}^n_+,\qquad v=0 \quad \text{on \;} \partial\mathbb{R}^n_+ \] is considered in the half space \(\mathbb{R}^n_+\). The parameter \(\lambda\) belongs to the sector \[ \Sigma_{\varepsilon}= \{\lambda\in C\setminus\{0\}:\;| \text{arg}\,\lambda| <\pi-\varepsilon\},\quad 0<\varepsilon<\frac{\pi}2. \] The solvability and uniqueness of the solution is established in weighted Muckenhoupt classes. Precise estimates to solutions are obtained. These estimates are the base to study \(L^p\)-regularity of the Stokes operator in a bounded domain in a forthcoming paper of the author.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D03
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 46E25
zbMATH DE Number: 1971865
zbMATH Keywords: Stokes resolvent problem
zbMATH Keywords: solvability
zbMATH Keywords: uniqueness
zbMATH Keywords: weighted Muckenhoupt classes
zbMATH Keywords: estimates
reviewed by: Il'ya Sh. Mogilevskii
MaRDI profile type: Publication
full work available at URL: s00021-003-0080-8
OpenAlex ID: W1654491902
DOI: 10.1007/S00021-003-0080-8
description: scientific article; zbMATH DE number 1971865