  This paper is devoted to the proof of a well-posedness result for the gravity
water waves equations, in arbitrary dimension and in fluid domains with general
bottoms, when the initial velocity field is not necessarily Lipschitz.
Moreover, for two-dimensional waves, we can consider solutions such that the
curvature of the initial free surface does not belong to $L^2$.
  The proof is entirely based on the Eulerian formulation of the water waves
equations, using microlocal analysis to obtain sharp Sobolev and H\"older
estimates. We first prove tame estimates in Sobolev spaces depending linearly
on H\"older norms and then we use the dispersive properties of the water-waves
system, namely Strichartz estimates, to control these H\"older norms.
