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- W1978332302 abstract "We study the Stokes problem of incompressible fluid dynamics in two and three-dimension spaces, for general bounded domains with smooth boundary. We use the vorticity–velocity-pressure formulation and introduce a new Hilbert space for the vorticity. We develop an abstract mixed formulation that gives a precise variational frame and conducts to a well-posed Stokes problem involving a new velocity–vorticity boundary condition. In the particular case of simply connected bidimensional domains with homogeneous boundary conditions, the link with the classical stream function-vorticity formulation is completely described, and we show that the vorticity–velocity-pressure formulation is a natural mathematical extension of the previous one.Nous étudions le problème de Stokes pour les fluides incompressibles en deux et trois dimensions, sur des domaines bornés à frontière régulière. Nous utilisons pour cela une formulation tourbillon–vitesse-pression et nous introduisons un nouvel espace de Hilbert pour le tourbillon. Nous développons une formulation mixte abstraite qui donne un cadre variationnel précis et conduit à un problème de Stokes bien posé faisant intervenir une nouvelle condition limite en vitesse–tourbillon. Dans le cas particulier de domaines bidimensionnels simplement connexes avec des conditions aux limites homogènes, nous décrivons complètement le lien avec la formulation classique en fonction courant-tourbillon et nous montrons que la formulation tourbillon–vitesse-pression est une extension mathématique naturelle de celle-ci." @default.
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- W1978332302 date "1995-09-01" @default.
- W1978332302 modified "2023-10-18" @default.
- W1978332302 title "On the velocity-vorticity formulation of the stokes system in two and three-dimension spaces" @default.
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- W1978332302 doi "https://doi.org/10.1016/0093-6413(95)00055-v" @default.
- W1978332302 hasPublicationYear "1995" @default.
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