Dispersive Estimates for Linearized Water Wave-Type Equations in Rd

We derive a L-x(1)(R-d)-L-x(infinity)(R-d) decay estimate of order O ( t(-d/2)) for the linear propagators [GRAPHICS] . with a loss of 3d/4 or d/4-derivatives in the case ss = 0 or ss = 1, respectively. These linear propagators are known to be associated with the linearized water wave equations, where the parameter ss measures surface tension effects. As an application, we prove low regularity well-posedness for a Whitham-Boussinesq-type system in R-d, d >= 2. This generalizes a recent result by Dinvay, Selberg and the third author where they proved low regularity well-posedness in R and R-2.