EXACT CONTROLLABILITY OF THE MOVEMENT OF NON-HOMOGENEOUS INCOMPRESSIBLE VISCOUS FLUID IN AN INFINITE CYLINDER

The aim of this work is to establish the exact controllability for a movement with axial symmetry of an incompressible non-homogeneous viscous fluid in an infinite cylinder. We assume that the tangential component of the velocity vector is zero for points which are located on the same circumference. We could simplify the Navier-Stokes system, thanks to the passage from rectangular coordinates to polar coordinates. The partial derivative equation becomes linear with one single spatial coordinate. By applying the theory of moments and the theory of exponential sums and using techniques specific of controllability for parabolic equations for one spatial dimension, The exact controllability is deduced.