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Existence for a two-dimensional, steady state fluid-structure interaction problem. (Existence et unicité de solutions d’un problème de couplage fluide-structure bidimensionnel stationnaire.) (French. Abridged English version) Zbl 0919.73139
Summary: We study the well-posedness of a steady-state problem: we consider a two-dimensional viscous incompressible flow, which is modeled by the Stokes equations. The structure is one-dimensional, and the equations describing the behaviour of elastic medium are beam equations. The fluid domain is defined by the shape of the structure function, resulting from a stress distribution coming from the fluid. The problem is thus nonlinear, and the equations we deal with are coupled. We prove its solvability through Schauder’s fixed point theorem.

74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D07 Stokes and related (Oseen, etc.) flows
35Q72 Other PDE from mechanics (MSC2000)
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