Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid. (English) Zbl 1260.35258
Summary: In this paper we study a three-dimensional fluid-structure interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations and we consider for the elastic structure a finite dimensional approximation of the equation of linear elasticity. The time variation of the fluid domain is not known a priori, so we deal with a free boundary value problem. Our main result yields the local in time existence and uniqueness of strong solutions for this system.
MSC:
35R35 | Free boundary problems for PDEs |
35Q30 | Navier-Stokes equations |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
37N15 | Dynamical systems in solid mechanics |
76D05 | Navier-Stokes equations for incompressible viscous fluids |