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Type: Artigo de periódico
Title: Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
Author: Guillen-Gonzalez, F
Rodriguez-Bellido, MA
Rojas-Medar, MA
Abstract: The main subject of this work is to study the concept of very weak solution for the hydrostatic Stokes system with mixed boundary conditions (non-smooth Neumann conditions on the rigid surface and homogeneous Dirichlet conditions elsewhere on the boundary). In the Stokes framework, this concept has been studied by Conca [Rev. Mat. Apl. 10 (1989)] imposing non-smooth Dirichlet boundary conditions. In this paper, we introduce the dual problem that turns out to be a hydrostatic Stokes system with non-free divergence condition. First, we obtain strong regularity for this dual problem (which can be viewed as a generalisation of the regularity results for the hydrostatic Stokes system with free divergence condition obtained by Ziane [Appl. Anal. 58 (1995)]). Afterwards, we prove existence and uniqueness of very weak solution for the (primal) problem. As a consequence of this result, the existence of strong solution for the non-stationary hydrostatic Navier-Stokes equations is proved, weakening the hypothesis over the time derivative of the wind stress tensor imposed by Guillen-Gonzalez, Masmoudi and Rodriguez-Bellido [Differential Integral Equations 50 (2001)]. (C) 2004 Elsevier SAS. All rights reserved.
Subject: hydrostatic Stokes equations
mixed boundary conditions
non-smooth boundary data
transposition method
Country: França
Editor: Gauthier-villars/editions Elsevier
Rights: aberto
Identifier DOI: 10.1016/j.anihpc.2003.11.002
Date Issue: 2004
Appears in Collections:Unicamp - Artigos e Outros Documentos

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