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We show the local null-controllability of a fluid-structure interaction system coupling a viscous incompressible fluid with a damped beam located on a part of its boundary. The controls act on arbitrary small parts of the fluid domain and of the beam domain. In order to show the result, we first use a change of variables and a linearization to reduce the problem to the null-controllability of a Stokes-beam system in a cylindrical domain. We obtain this property by combining Carleman inequalities for the heat equation, for the damped beam equation and for the Laplace equation with high-frequency estimates. Then, the result on the nonlinear system is obtained by a fixed-point argument. [ABSTRACT FROM AUTHOR]

We analyze a bidimensional fluid-structure interaction system composed of a viscous incompressible fluid and a beam located at the boundary of the fluid domain. Our main result is the existence and uniqueness of strong solutions for the corresponding coupled system. The proof is based on a the study of the linearized system and a fixed point procedure. In particular, we show that the linearized system can be written with a Gevrey class semigroup. The main novelty with respect to previous results is that we do not consider any approximation in the beam equation. [ABSTRACT FROM AUTHOR]

We study the boundary controllability of 2×2 system of heat equations by using a flatness approach. According to the relation between the diffusion coefficients of the heat equation, it is known that the system can be neither null-controllable nor null-controllable for any T>T0, where T0∈[0,∞]. Here we recover this result in the case that T0∈[0,∞) by using the flatness method, and we obtain an explicit formula for the control and for the corresponding solutions. In particular, the state and the control have Gevrey regularity in time and in space. [ABSTRACT FROM AUTHOR]

We propose a new model in a fluid-rigid structure system composed by a rigid body and a viscous incompressible fluid using a boundary condition based on Coulomb's law. This boundary condition allows the fluid to slip on the boundary if the tangential component of the stress is too large. In the opposite case, we recover the standard Dirichlet boundary condition. The governing equations are the Navier-Stokes system for the fluid and the Newton laws for the body. The corresponding coupled system can be written as a variational inequality. We prove that there exists a weak solution of this system. [ABSTRACT FROM AUTHOR]

We consider the geometrical inverse problem consisting in recovering an unknown obstacle in a viscous incompressible fluid by measurements of the Cauchy force on the exterior boundary. We deal with the case where the fluid equations are the nonstationary Stokes system and using the enclosure method, we can recover the convex hull of the obstacle and the distance from a point to the obstacle. With the same method, we can obtain the same result in the case of a linear fluid-structure system composed by a rigid body and a viscous incompressible fluid. We also tackle the corresponding nonlinear systems: the Navier-Stokes system and a fluid-structure system with free boundary. Using complex spherical waves, we obtain some partial information on the distance from a point to the obstacle. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system modeling the interaction between a viscous incompressible fluid and an elastic structure. The fluid motion is represented by the classical Navier–Stokes equations while the elastic displacement is described by the linearized elasticity equation. The elastic structure is immersed in the fluid and the whole system is confined into a general bounded smooth domain of . Our main result is the local in time existence and uniqueness of a strong solution of the corresponding system. [ABSTRACT FROM AUTHOR]