  We prove a dispersive estimate for the solutions of the linearized
Water-Waves equations in dimension 1 in presence of a flat bottom. We prove a
decay with respect to time t of order 1/3 for solutions with initial data in
weighted Sobolev spaces. We also give variants to this result with different
decays for a more convenient use of the dispersive estimate. We then give an
existence result for the full Water-Waves equations in weighted spaces for
practical uses of the proven dispersive estimates.
