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

Tilahun Deneke, Tamirat T. Dufera, Achenef Tesfahun

We derive a $L_x^1({\mathbb{R}}^d)-L_x^{\infty }({\mathbb{R}}^d)$ decay estimate of order $\mathcal{O}\left(t^{-d/2}\right)$ for the linear propagators $$\exp \left( {\pm it \sqrt{ |D…