Abstract

We study an unsteady nonlinear fluid-structure interaction problem where a two-dimensional viscous incompressible Newtonian fluid and a one-dimensional elastic structure, located on one part of the fluid domain boundary, interact. The fluid motion is modeled by the two-dimensional incompressible Navier–Stokes equations set in an unknown domain which depends on the structure’s displacement. We consider longitudinal as well as transversal structure displacement. We assume that the longitudinal displacement of the structure satisfies a wave equation whereas the transversal displacement follows a beam equation with inertia of rotation. The fluid and structure systems are coupled through a kinematic condition which corresponds to a no-slip condition at the fluid-structure interface and the fluid exerts a force on the elastic structure. We prove the existence and uniqueness of strong solution to the considered problem with no gap between the initial conditions regularity and the ones obtained in positive time. To our knowledge, this is the first result regarding existence and uniqueness of strong solutions for fluid-beam interaction problem in the unsteady case taking into account both the transversal displacement and the longitudinal structure displacement.

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