  We investigate the stabilization of a multidimensional system of coupled wave
equations with only one Kelvin Voigt damping. Using a unique continuation
result based on a Carleman estimate and a general criteria of Arendt Batty, we
prove the strong stability of the system in the absence of the compactness of
the resolvent without any geometric condition. Then, using a spectral analysis,
we prove the non uniform stability of the system. Further, using frequency
domain approach combined with a multiplier technique, we establish some
polynomial stability results by considering different geometric conditions on
the coupling and damping domains. In addition, we establish two polynomial
energy decay rates of the system on a square domain where the damping and the
coupling are localized in a vertical strip.
