We consider the so-called transport-Stokes system which describes sedimentation of
inertialess suspensions in a viscous flow and couples a transport equation and the steady …

In this work, we investigate the small-time global exact controllability of the Navier–Stokes
equation, both towards the null equilibrium state and towards weak trajectories. We consider …

A result concerning the global approximate controllability of the Navier–Stokes system in
dimension 3 Page 1 Available online at www.sciencedirect.com J. Math. Pures Appl. 98 (2012) …

In the Eulerian approach, the motion of an incompressible fluid is usually described by the
velocity field which is given by the Navier–Stokes system. The velocity field generates a flow …

We establish a result concerning the so-called Lagrangian controllability of the Euler
equation for incompressible perfect fluids in dimension 3. More precisely, we consider a …

We deal with the 3D Navier–Stokes equation in a smooth simply connected bounded
domain, with controls on a non-empty open part of the boundary and a Navier slip-with …

We consider the motion of a rigid body immersed in a two-dimensional irrotational perfect
incompressible fluid. The fluid is governed by the Euler equation, while the trajectory of the …

In this paper, we establish a result of Lagrangian controllability for a fluid at low Reynolds
number, driven by the stationary Stokes equation. This amounts to the possibility of …

We consider in this paper the problem of the Lagrangian controllability for the KdV equation.
Using the N-solitons solution, we prove that, for any length of the spatial domain L>0 and …

The goal of these lecture notes is to present some techniques of non-linear control of PDEs,
in the context of fluid mechanics. We will consider the problem of controllability of two …