\(L^p\)-weighted theory for Navier-Stokes equations in exterior domains
type: Item
instance of: scholarly article
title: \(L^p\)-weighted theory for Navier-Stokes equations in exterior domains
zbMATH Open document ID: 1179.35206
author: Chérif Amrouche
author: Nguyen Huy Hoang
published in: Communications in Mathematical Analysis
publication date: 2009-10-06T00:00:00Z
review text: In this very interesting and technical paper, the exterior Navier-Stokes problem is considered. The flow is studied in an unbounded domain; the no-slip condition is considered on a part of boundary. Very important is the imposed behaviour of the velocity at infinity. The point is to improve some previous result of Farwing and Galdi, where the external force field \(f\) was considered in a classical \(L^p\) Lebesgue space. In the present paper, the external forces are considered in some generalized \(W\)-Sobolev spaces. For different regularity levels of \(f\), the corresponding existence and smoothness of the associated weak solutions are studied. The exterior Oseen problem is also considered. The important mathematical tools used in this paper are the unit partition result (introduced in Proposition 8) and some energetic inequalities.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 5610815
zbMATH Keywords: Navier-Stokes equation
zbMATH Keywords: Oseen problem
zbMATH Keywords: unbounded domains
zbMATH Keywords: weighted Sobolev spaces
reviewed by: Gelu Paşa
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5610815