Variational methods for fluid-structure interaction and porous media. (English) Zbl 1519.76319
Summary: In this work we consider a poroelastic, flexible material that may deform largely, which is situated in an incompressible fluid driven by the Navier-Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms.
MSC:
| 76S05 | Flows in porous media; filtration; seepage |
| 76M30 | Variational methods applied to problems in fluid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 74A30 | Nonsimple materials |
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
fluid-poroelastic structure interaction; large deformation; incompressible Navier-Stokes equations; existence; weak solution; Fréchet derivative; non-convex energy functional; non-simple elastic solidReferences:
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