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On the three‐dimensional stationary exterior Stokes problem with non standard boundary conditions
Author(s) -
Louati Hela,
Meslameni Mohamed,
Razafison Ulrich
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900181
Subject(s) - uniqueness , mathematics , boundary (topology) , mathematical analysis , domain (mathematical analysis) , boundary value problem , stokes problem , infinity , flow (mathematics) , slip (aerodynamics) , set (abstract data type) , geometry , computer science , physics , finite element method , thermodynamics , programming language
Abstract We study the three‐dimensional stationary exterior Stokes problem with non standard boundary conditions corresponding to a slip‐without‐friction boundary conditions. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of solutions. This functional framework allows to prescribe various behaviors at infinity of the solutions. The established results are related to the existence and the uniqueness of strong and very weak solutions. Our strategy relies on the fact that due to the boundary conditions, the pressure and the velocity can be decoupled and, as a result, we solve two separate systems to find these quantities.