EXACT CONTROLLABILITY OF THE MOVEMENT OF NON-HOMOGENEOUS INCOMPRESSIBLE VISCOUS FLUID IN AN INFINITE CYLINDER
DJAHIDA HIBER *
Department of Mathematics, University of Sciences and Technology of Oran, P.O.Box 1505, EL Mnaouar, Bir EL Djir, Oran, 31000, Algeria.
DALILA REMAOUN BOUREGA
Department of Mathematics, University of Sciences and Technology of Oran, P.O.Box 1505, EL Mnaouar, Bir EL Djir, Oran, 31000, Algeria.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Exact controllability, hilbert space, movement of non-homogeneous incompressible viscous fluid, moment theory, systems of Navier-Stokes, theory of Müntz.