Page 502 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 502
MATHEMATICAL ANALYSIS: THE INTERACTION OF FLUIDS/ VISCOELASTIC
MATERIALS AND SOLIDS (MS-36)
On the Exponential Stability of A Compressible FSI PDE System
Pelin Guven Geredeli, peling@iastate.edu
Iowa State University, United States
We consider a linearized compressible flow structure interaction (FSI) PDE model with a view
of analyzing the stability properties of both the compressible flow and plate solution compo-
nents. We operate in the time domain by way of obtaining the necessary energy estimates which
culminate in an alternative proof for the uniform stability of finite energy compressible flow-
structure solutions. Unlike the frequency domain approach followed in the earlier papers, we
give the proof of our stability result in time domain via an approach which involves a gradient
type multiplier to obtain the necessary energy estimates.
Description of contacts in fluid-beam systems
Matthieu Hillairet, matthieu.hillairet@umontpellier.fr
Universite Montpellier, France
In this talk we consider a family of systems describing the interactions between a film of fluid
deposited on a horizontal substrate and a beam delimiting the upper boundary of the film. The
fluid motion is prescribed by solving the incompressible Navier Stokes equations. The beam
is assumed to move vertically only, several models are proposed depending on whether damp-
ing/viscosity terms are included or not. The coupling between the fluid and the beam is imposed
via the continuity of velocity-fields and normal stress.
Such systems have been thorouhgly studied in the recent years especially to develop a
Cauchy for strong/weak solutions up to the possible first time of contact between the moving
beam and the substrate. In this talk, we will focus on the decription of beam/substrate con-
tact. We will first discuss finite-time occurence and then provide a Cauchy theory that handle
contacts. This talk is based on collaborations with C. Grandmont (INRIA Paris), J. Lequeurre
(Univ. Lorraine) and J-J Casanova (Univ. Paris Dauphine)
Motion of a Rigid body in a Compressible Fluid
Arnab Roy, royarnab244@gmail.com
Institute of Mathematics of the Czech Academy of Sciences, Czech Republic
In this talk, we discuss the motion of a rigid body in a bounded domain which is filled with a
compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface
as well as at the boundary of the domain. We prove existence of a weak solution of the fluid-
structure system up to collision.
500
MATERIALS AND SOLIDS (MS-36)
On the Exponential Stability of A Compressible FSI PDE System
Pelin Guven Geredeli, peling@iastate.edu
Iowa State University, United States
We consider a linearized compressible flow structure interaction (FSI) PDE model with a view
of analyzing the stability properties of both the compressible flow and plate solution compo-
nents. We operate in the time domain by way of obtaining the necessary energy estimates which
culminate in an alternative proof for the uniform stability of finite energy compressible flow-
structure solutions. Unlike the frequency domain approach followed in the earlier papers, we
give the proof of our stability result in time domain via an approach which involves a gradient
type multiplier to obtain the necessary energy estimates.
Description of contacts in fluid-beam systems
Matthieu Hillairet, matthieu.hillairet@umontpellier.fr
Universite Montpellier, France
In this talk we consider a family of systems describing the interactions between a film of fluid
deposited on a horizontal substrate and a beam delimiting the upper boundary of the film. The
fluid motion is prescribed by solving the incompressible Navier Stokes equations. The beam
is assumed to move vertically only, several models are proposed depending on whether damp-
ing/viscosity terms are included or not. The coupling between the fluid and the beam is imposed
via the continuity of velocity-fields and normal stress.
Such systems have been thorouhgly studied in the recent years especially to develop a
Cauchy for strong/weak solutions up to the possible first time of contact between the moving
beam and the substrate. In this talk, we will focus on the decription of beam/substrate con-
tact. We will first discuss finite-time occurence and then provide a Cauchy theory that handle
contacts. This talk is based on collaborations with C. Grandmont (INRIA Paris), J. Lequeurre
(Univ. Lorraine) and J-J Casanova (Univ. Paris Dauphine)
Motion of a Rigid body in a Compressible Fluid
Arnab Roy, royarnab244@gmail.com
Institute of Mathematics of the Czech Academy of Sciences, Czech Republic
In this talk, we discuss the motion of a rigid body in a bounded domain which is filled with a
compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface
as well as at the boundary of the domain. We prove existence of a weak solution of the fluid-
structure system up to collision.
500
