caa a22 4500 388109068 CHVBK 20180307125348.0 cr unu---uuuuu 161130s1999 xx s 000 0 eng 10.1017/S0308210500013159 doi S0308210500013159 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500013159 Konate Dialla LICIA, 37 Rue de la République, 92800 Puteaux, France (dkonate@wanadoo.fr) Asymptotic solution for the perturbed Stokes problem in a bounded domain in two and three dimensions [Elektronische Daten] [Dialla Konate] We consider the Stokes problem with a small viscosity. When the viscosity goes to zero, the boundary-layer phenomenon can appear. In this case, the solution of the given perturbed Stokes equation cannot be properly approximated by the solution of its limiting equation ‘near' the boundary Γ of the domain of study, say Ω To overcome this problem, we need to construct a corrector term in the neighbourhood of Γ Lions has studied this problem and has constructed a corrector for the case where Ω is a half space in ℝ2. The case where Ω is an open and bounded domain of ℝ2 or ℝ3, which remained unsolved, is the concern of this paper. The construction of the corrector to the perturbed Stokes equation depends heavily on the geometry of Ω In two dimensions, we construct the corrector in the form of a stream function, while in ℝ3 we construct it in the form of a potential vector. The corrector acts effectively in a neighbourhood of Γ that is the boundary layer. Using similar methods to those of Baranger and Tartar, we define the thickness of the boundary layer in a natural way. In addition, in this paper we study the behaviour of the corrected solution in some Hölder spaces. Copyright © Royal Society of Edinburgh 1999 Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 811-824 0308-2105 129:4<811 1999 129 PRM https://doi.org/10.1017/S0308210500013159 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500013159 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Konate Dialla LICIA, 37 Rue de la République, 92800 Puteaux, France (dkonate@wanadoo.fr) NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 129/4(1999), 811-824 0308-2105 129:4<811 1999 129 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge