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Existence for a three-dimensional steady-state fluid-structure interaction problem. (English) Zbl 1009.76016
Summary: A steady state fluid-structure interaction problem is considered, and its solvability is studied. Both the fluid and the structure are three-dimensional. The equations of viscous fluid motion are set in an unknown domain depending on structure displacement. The structure is elastic, and its deformation depends on the stress coming from the fluid. We prove that, for small enough applied exterior forces, there exists at least one regular solution of this nonlinear coupled problem.

MSC:
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D07 Stokes and related (Oseen, etc.) flows
35Q30 Navier-Stokes equations
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