Weak solutions for a fluid-elastic structure interaction model. (English) Zbl 1007.35055
The purpose is to study a model coupling an incompressible viscous Navier-Stokes fluid with a linearly elastic structure in a bounded container. Using Leray-Schauder technique, energy estimates and compactness argument, the authors prove the existence of weak solutions and investigate their stability. An important part of the proof is the representation of global Eulerian velocity by functions defined in fixed reference domains.
Reviewer: Oleg Titow (Berlin)
MSC:
35Q30 | Navier-Stokes equations |
35Q72 | Other PDE from mechanics (MSC2000) |
74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
76D05 | Navier-Stokes equations for incompressible viscous fluids |