Artículos de revistas
Hydrostatic Stokes equations with non-smooth data for mixed boundary conditions
Registro en:
Annales De L Institut Henri Poincare-analyse Non Lineaire. Gauthier-villars/editions Elsevier, v. 21, n. 6, n. 807, n. 826, 2004.
0294-1449
WOS:000224946500003
10.1016/j.anihpc.2003.11.002
Autor
Guillen-Gonzalez, F
Rodriguez-Bellido, MA
Rojas-Medar, MA
Institución
Resumen
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. 21 6 807 826