Dispersive estimates for linearized water wave type equations in $\mathbb R^d$

Abstract

with a loss of 3d/4 or d/4 -derivatives in the case β = 0 or β = 1, respectively. These linear propagators are known to be associated with the linearized water wave equations, where the parameter β 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 .