  In this paper, we investigate the direct and indirect stability of locally
coupled wave equations with local viscous damping on cylindrical and
non-regular domains without any geometric control condition. If only one
equation is damped, we prove that the energy of our system decays polynomially
with the rate $t^{-\frac{1}{2}}$ if the two waves have the same speed of
propagation, and with rate $t^{-\frac{1}{3}}$ if the two waves do not propagate
at the same speed. Otherwise, in case of two damped equations, we prove a
polynomial energy decay rate of order $t^{-1}$.
