“…Different with the control introduced in the system (1.4), Alazard discussed in [6] the stabilization of the nonlinear water waves system in a rectangle where the external pressure as the control signal acts on a part of the free surface, by absorbing the waves coming from the left. For the problem in a cubic domain, in an irregular domain and the case of the water waves with surface tension, please refer to Reid [7] and [8], Craig et al [9], Alazard et al [10] and [11]. Recently, for u ∈ L 2 loc [0, ∞), we established in our paper [1] the well-posedness of the system (1.4), and further showed that it can be recast as a well-posed linear control system (for this concept, please refer to [1], Weiss [12] or Tucsnak and Weiss [13]).…”