# Registered Data

## [00558] Bifurcations, periodicity and stability in fluid-structure interactions

**Session Date & Time**:- 00558 (1/3) : 1C (Aug.21, 13:20-15:00)
- 00558 (2/3) : 1D (Aug.21, 15:30-17:10)
- 00558 (3/3) : 1E (Aug.21, 17:40-19:20)

**Type**: Proposal of Minisymposium**Abstract**: This minisymposium connects rigorous mathematical theory with empirically observed time-periodic phenomena arising in fluid-structure interactions. Scenarios of interest include: aeroelastic resonances and flutter instabilities, e.g., bridge deck and flight-structure instabilities, and nonlinear phenomena such as von Karman vortex sheets, and the various approaches which have been developed such as spectral analyses and theories of weak solutions. Theoretical advances are complemented by progress in numerical simulation. We facilitate the connections between experts of various mathematical backgrounds for the development of new strategies exploiting the interplay between different approaches. Lastly, we wish to emphasize open problems in this challenging and exciting area.**Organizer(s)**: Boris Muha, Sebastian Schwarzacher, Justin Webster**Classification**:__74F10__,__35Q35__,__70K20__,__35B40__,__65Mxx__**Speakers Info**:- Sunčica Čanić (UC Berkeley)
- Giusy Mazzone (Queen's University)
- Marius Tucsnak (University of Bordeaux)
- Irena Lasiecka (University of Memphis)
- Thomas Eiter (Weierstrass Institute for Applied Analysis and Stochastics)
- George Avalos (University of Nebraska-Lincoln)
- Eduard Feireisl (Institute of Mathematics, Czech Academy of Sciences)
- Srđan Trifunović (University of Novi Sad)
- Jaroslav Hron (Charles University, Prague)
- Sebastian Schwarzacher (Uppsala University)
- Justin Webster (University of Maryland, Baltimore County)
**Boris Muha**(University of Zagreb)

**Talks in Minisymposium**:**[02192] Modelling and analysis of solids floating in a viscous fluid****Author(s)**:**Marius Tucsnak**(University of Bordeaux)

**Abstract**: We describe some recent advances on the mathematical modelling of the interaction of water waves with floating objects. The main applications we have in mind are point absorber type devices for producing marine energy and floating platforms used to support wind turbines. The mathematical challenge here is the existence of two free boundaries: the free surface of the fluid and the solid-fluid interface. The presentation is essentially devoted to wellposedness and large time behavior issues.

**[02207] Time-periodic solutions to an interaction problem between a compressible fluid and a viscoelastic structure****Author(s)**:**Srđan Trifunović**(Faculty of Sciences, University of Novi Sad)- Šárka Nečasová (Institute of Mathematics AS CR)
- Ondřej Kreml (Institute of Mathematics AS CR)
- Václav Mácha (Institute of Mathematics AS CR)

**Abstract**: In this lecture, I will talk about the problem of interaction between a compressible fluid and a viscoelastic beam under the influence of time-periodic external forces in 2D. For this problem, at least one weak solution is constructed which is periodic in time and perserves the mass which is a given constant. The approximate solution is obtained via a decoupling scheme in finite bases for time and space.

**[02722] Artificial boundary conditions for time-periodic flow past a body****Author(s)**:**Thomas Eiter**(Weierstrass Institute for Applied Analysis and Stochastics)

**Abstract**: Consider the time-periodic viscous flow past an obstacle. Numerical implementations require to reduce the problem to a bounded domain by introducing an artificial boundary. In this talk, we study a choice of associated boundary conditions such that this perturbed problem suitably approximates the original one. These boundary conditions reflect the asymptotic behavior of the flow, which is studied in terms of new representation formulas relying on time-periodic fundamental solutions to the linearized Navier-Stokes equations.

**[04678] Weak solutions in fluid-structure interactions: Cauchy and periodic problems****Author(s)**:**Boris Muha**(University of Zagreb)- Sebastian Schwarzacher (Charles University and Uppsala University)
- Justin Thomas Webster (University of Maryland, Baltimore County)

**Abstract**: In this talk, we will provide an overview of the latest developments in the theory of weak solutions to fluid-structure interaction problems. We will specifically explore the difficulties and distinctions that arise when moving from the Cauchy problem to that of obtaining periodic solutions. We will examine a simple heat-wave system, which serves as a representative example for a fluid-structure interactions; for this system, we present some new existence results for periodic solutions.

**[04833] On the motion of several small rigid bodies in a viscous incompressible fluid****Author(s)**:**Eduard Feireisl**(Czech Academy of Sciences)

**Abstract**: We consider the motion of N rigid bodies immersed in a viscous incompressible fluid contained in a domain in the Euclidean space Rd, d = 2; 3. We show the fluid flow is not influenced by the presence of the bodies in the asymptotic limit as when the radius of the bodies tends to zero sufficiently fast. The result depends solely on the geometry of the bodies and is independent of their mass densities. Collisions are allowed and the initial data are arbitrary with finite energy.

**[05105] On the motion of a fluid-filled elastic solid****Author(s)**:**Giusy Mazzone**(Queen's University)

**Abstract**: Consider the physical system constituted by an elastic solid with an interior cavity entirely filled by a viscous incompressible fluid. The motion of the coupled system is governed by the Navier equations of linear elasticity for the solid, and the Navier-Stokes equations for the fluid. Continuity of stresses and velocities are imposed at the fluid-solid interface, while a zero-traction condition is imposed at the other free boundary of the solid. I will present some results on the existence of strong solutions to the governing equations and discuss their stability properties.

**[05124] Gevrey regularity of a certain fluid-structure PDE interaction****Author(s)**:**George Avalos**(University of Nebraska-Lincoln)

**Abstract**: In this talk, we present recent results concerning the qualitative behavior of a coupled partial differential equation (PDE) system which describes a certain fluid-structure interaction (FSI), as it occurs in nature. With respect to the associated strongly continuous contraction semigroup for this model, we present our recent results of Gevrey regularity.

**[05184] Numerical benchmarking of FSI - efficient discretization and numerical solution****Author(s)**:**Jaroslav Hron**(Charles University, Prague)

**Abstract**: The lecture will give an overview of the problem of fluid-structure interaction motivated by blood flow in deformable vessels. Possible discretizations by the finite element method and different coupling strategies will be discussed with a focus on the efficient numerical solution of the monolithic problem. We will discuss some simple benchmark type problems of fluid structure interaction based on finding a suitable simple arrangement with self-induced oscillations.