Olivier Glass

On the controllability of the 1-D isentropic Euler equation

We study the controllability problem for the one-dimensional Euler isentropic system, both in Eulerian and Lagrangian coordinates, by means of boundary controls, in the context of weak entropy solutions. We give a sufficient condition on the initial and final states under which the first one can be steered to the latter.

On the Uniform Controllability of the Burgers Equation

In this paper, we deal with the viscous Burgers equation with a small dissipation coefficient

Exact Boundary Controllability for 1-D Quasilinear Hyperbolic Systems with a Vanishing Characteristic Speed

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Controllability of the Korteweg–de Vries equation from the right Dirichlet boundary condition

. We prove the (global) exact controllability property to nonzero constant states, that is to say, the possibility of finding boundary values such that the solution of the associated Burgers equation is driven to a constant state. The main objective of this paper is to do so with control functions whose norms in an appropriate space are bounded independently of

Asymptotic Stabilizability by Stationary Feedback of the Two-Dimensional Euler Equation: The Multiconnected Case

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On the motion of a rigid body in a two-dimensional irregular ideal flow

, which belongs to a suitably small interval. This result is obtained for a sufficiently large time.

Uniform controllability of a transport equation in zero di ffusion-dispersion limit

The general theory on exact boundary controllability for general first order quasilinear hyperbolic systems requires that the characteristic speeds of the system do not vanish. This paper deals with exact boundary controllability, when this is not the case. Some important models are also shown as applications of the main result. The strategy uses the return method, which allows one in certain situations to recover nonzero characteristic speeds.

An addendum to a J.M. Coron theorem concerning the controllability of the Euler system for 2D incompressible inviscid fluids

In this paper, we consider the controllability of the Korteweg–de Vries equation in a bounded interval when the control operates via the right Dirichlet boundary condition, while the left Dirichlet and the right Neumann boundary conditions are kept to zero. We prove that the linearized equation is controllable if and only if the length of the spatial domain does not belong to some countable critical set. When the length is not critical, we prove the local exact controllability of the nonlinear equation.

On the control of the motion of a boat

We construct a feedback law which allows us to asymptotically stabilize the Euler system for incompressible inviscid fluids in two dimensions, in the case of a multiconnected bounded domain, by means of a control localized on a part of the boundary that meets every connected component of the boundary. This generalizes a result of Coron [{SIAM J. Control Optim., 37 (1999), pp. 1874--1896] concerning simply connected domains.

The movement of a solid in an incompressible perfect fluid as a geodesic flow

We consider the motion of a rigid body immersed in an ideal flow occupying the plane with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time in the spirit of the famous work by Yudovich for the fluid alone. We prove that if the bodys boundary is Gevrey, then the bodys trajectory is Gevrey. This extends the previous work of Glass, Sueur, and Takahashi [Ann. Sci. Ecole Norm. Sci. (4), 45 (2012), pp. 1--51] to a case where the flow is irregular.