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A stream‐function–vorticity variational formulation for the exterior Stokes problem in weighted Sobolev spaces
Author(s) -
Girault V.,
Giroire J.,
Sequeira A.
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150506
Subject(s) - sobolev space , mathematics , stream function , bounded function , vorticity , domain (mathematical analysis) , mathematical analysis , function (biology) , stokes problem , vector valued function , function space , pure mathematics , vortex , physics , evolutionary biology , finite element method , biology , thermodynamics
In this paper we derive a mixed variational formulation for the exterior Stokes problem in terms of the vorticity and stream function, or the vector potential in three dimensions. The main steps are the construction of the stream function (or vector potential) and the proof of the Babuška–Brezzi ‘inf‐sup’ condition. The two‐ and three‐dimensional cases are treated separately because the structure of the stream function differs substantially according to the number of dimensions considered. The conclusion of this work is that if the problem is set in the weighted Sobolev spaces of Hanouzet and Giroire, the analysis of the exterior Stokes problem is quite the same as if the domain were bounded.