Stokes equations and elliptic systems with nonstandard boundary conditions
type: Item
instance of: scholarly article
title: Stokes equations and elliptic systems with nonstandard boundary conditions
zbMATH Open document ID: 1230.35083
author: Chérif Amrouche
author: Nour El Houda Seloula
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2011-07-08T00:00:00Z
review text: The incompressible Navier-Stokes equations with nonstandard boundary conditions \({\mathbf u} \cdot {\mathbf n} =0\), \(\mathrm{curl} ({\mathbf u}) \times {\mathbf u}=0\) were studied in [\textit{V. Girault}, Lect. Notes Math. 1431, 201--218 (1990; Zbl 0702.76037)]. The present paper concerns stationary Stokes equations in bounded, possibly multiple-connected domains, with similar nonhomogeneous non-standard boundary conditions. The existence and uniqueness of strong, weak and very weak solutions is proved using inf-sup conditions (based on the Necas inequality). The main contribution of the authors is to consider the above problem in non-Hilbert spaces \(L^p\).
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35D30
Mathematics Subject Classification ID: 35D35
zbMATH DE Number: 5919187
zbMATH Keywords: Stokes equations
zbMATH Keywords: 3D multiple connected domains
zbMATH Keywords: non homogeneous boundary conditions
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: j.crma.2011.04.007
OpenAlex ID: W2032267111
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DOI: 10.1016/J.CRMA.2011.04.007
description: scientific article; zbMATH DE number 5919187