In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given , the system can be driven at rest and the structure to its reference configuration at time . To show this result, we first consider a linearized system....
In this paper, we prove a controllability
result for a fluid-structure interaction problem. In dimension two,
a rigid structure moves into an incompressible fluid governed by
Navier-Stokes equations. The control acts on a fixed subset of the
fluid domain. We prove that, for small initial data, this system is
null controllable, that is, for a given , the system can be
driven at rest and the structure to its reference configuration at
time . To show this result, we first consider a linearized
system....
We study a non standard unique continuation property for the biharmonic spectral problem in a 2D corner with homogeneous Dirichlet boundary conditions and a supplementary third order boundary condition on one side of the corner. We prove that if the corner has an angle , and , a unique continuation property holds. Approximate controllability of a 2-D linear fluid-structure problem follows from this property, with a control acting on the elastic side of a corner in a domain containing a Stokes...
We consider a linear model of interaction between a viscous incompressible
fluid and a thin elastic structure located on a part of the fluid domain
boundary, the other part being rigid. After having given an existence and
uniqueness result for the direct problem, we study the question of
approximate controllability for this system when the control acts as a
normal force applied to the structure. The case of an analytic boundary has
been studied by Lions and Zuazua in [9]
where, in particular,...
We study a non standard unique continuation property for the
biharmonic spectral problem in a 2D
corner with homogeneous Dirichlet boundary conditions and a
supplementary third order boundary condition on one side of the
corner. We prove that if the corner has an angle ,
and , a unique continuation
property holds. Approximate controllability of a 2-D linear
fluid-structure problem follows from this property, with a control
acting on the elastic side of a corner in a domain containing...
Data assimilation refers to any methodology that uses partial observational data and the dynamics of a system for estimating the model state or its parameters. We consider here a non classical approach to data assimilation based in null controllability introduced in [Puel, 335 (2002) 161–166] and [Puel, 48 (2009) 1089–1111] and we apply it to oceanography. More precisely, we are interested in developing this methodology to recover the unknown final state value (state value at the end of the measurement...
Data assimilation refers to any methodology that uses partial
observational data and the dynamics of a system for estimating the
model state or its parameters. We consider here a non classical
approach to data assimilation based in null controllability
introduced in [Puel,
(2002) 161–166] and [Puel,
(2009) 1089–1111] and we apply it to oceanography.
More precisely, we are interested in developing this methodology
to recover the unknown final state value (state...
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