  We consider the gravity-capillary waves in any dimension and in fluid domains
with general bottoms. Using the paradiferential reduction established in the
companion paper, we prove Strichartz estimates for solutions to this problem,
at a low regularity level such that initially, the velocity field can be
non-Lipschitz up to the free surface. We then use those estimates to solve the
Cauchy problem at this level of regularity.
