This paper is divided into two parts and focuses on the linear independence of boundary traces of eigenfunctions of boundary value problems. Part I deals with second-order elliptic operators, and Part II with Stokes (and Oseen) operators. Part I: Let ${\lambda }_i$ be an eigenvalue of a second-order elliptic operator defined on an open, sufficiently smooth, bounded domain Ω in ℝⁿ, with Neumann homogeneous boundary conditions on Γ = tial Ω. Let ${{\phi }_{ij}}_{j=1}^{{\ell }_i}$ be the corresponding linearly independent (normalized) eigenfunctions...

In this talk, I will present a recent result obtained in [6] with O. Glass, S. Guerrero and J.-P. Puel on the local exact controllability of the $1$-d compressible Navier-Stokes equations. The goal of these notes is to give an informal presentation of this article and we refer the reader to it for extensive details.

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 $T\>0$, the system can be driven at rest and the structure to its reference configuration at time $T$. 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 T > 0, the system can be driven at rest and the structure to its reference configuration at time T. To show this result, we first consider a linearized system....