consider a 1-D tank containing an inviscid incompressible irrotational fluid.
The tank is subject to the control which consists of horizontal moves. We
assume that the motion of the fluid is well-described by the Saint-Venant
equations (also called the shallow water equations). We prove the local controllability
of this nonlinear control system around any steady state. As a corollary
we get that one can move from any steady state to any other steady state. Full paper.