Prescribing the motion of a set of particles in a 3D perfect fluid
This provides a theoretical foundation for controlling fluid motion at the particle level, relevant to fluid dynamics and control theory.
The paper proves that for a 3D incompressible perfect fluid, any given set of fluid particles can be approximately steered to any other set of the same volume using boundary controls, establishing Lagrangian controllability of the Euler equation.
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 connected bounded domain of R^3 and two smooth contractible sets of fluid particles, surrounding the same volume. We prove that given any initial velocity field, one can find a boundary control and a time interval such that the corresponding solution of the Euler equation makes the first of the two sets approximately reach the second one.