Abstract: In this talk, I will present a joint result with Kai Koike and Gaston Vergara-Hermosilla regarding the controllability of a viscous compressible barotropic flow in $1$D. More precisely we consider the compressible NS system on a bounded interval with homogeneous Dirichlet boundary conditions and with a constant rest state as initial data. We prove that it is possible to construct an appropriate force term $f$ such that some fluid particles of an initial subinterval move exactly to another close one at some given time $T>0$. Moreover this force can be chosen supported away from these particles, which means that we achieve an exact Lagrangian controllability result by the means of a remote action.
