Mathematical analysis for elastic shells interacting with fluids

Elastic shells interacting with fluidsWhenever a fluid is influencing the motion of a thin elastic object or vice-verse. A prominent example is the blood-flow through a vessel.

Other well studied examples are oil-flow through pipes, cell walls but also the deck of a suspension bridge or aeroplane wings.

Wider research contextThe project will build an analysis tailored to answer questions arising when(deformable elastic) solid shells are interacting with viscous fluids governed by the Navier-Stokes equations in two or three space dimensions. We consider both cases. A shell that is surrounded by a fluid and a shell that is a part of the fluid-boundary.

The challenge is summarized by the different structural discription between the two mattes and that the time changing interface of interaction itself is a part of the solution.Objectives and innovationWe aim to extend the theory on such interaction to study the global-in-time-existence, uniqueness, stability, and in particular the regularity for a wider class of elastic structure.

Further we investigate the appearance of periodic in times solutions (e.g. driven by the heart-beat). An emphasise is on the study of self-contact of the elastic shell.

General technical progress can be expected in the analysis for variable in time geometries and non-linear coupled systems of partial differential equations.