On the existence of solution for a nonhomogeneous Stokes-rod coupled problem Original Research Article

The existence of solution for a stationary fluid-structure interaction problem is stated. More precisely, the viscous incompressible fluid is governed by Stokes equations with nonhomogeneous Dirichlet boundary conditions on the velocity. The elastic structure occupies the upper boundary of the fluid domain and it is governed by a rod model. The coupling is given by the fluid pressure acting as an external force on the rod and the rod displacement modifying the initial fluid domain. After passing to homogeneous boundary conditions by lifting and lagrangean coordinates for Stokes equations, the existence of solution in the appropriate functional spaces follows from a fixed point iteration between both models. Norm estimates and regularity on the solution of each model are essential to apply the fixed point theorem. In this way, the technique also provides estimates for the rod displacement, the fluid pressure and velocity.