Existence and scattering of small solutions to a Boussinesq type equation of sixth order

In this paper, we consider the existence and uniqueness of the global small solution as well as the small data scattering result to the Cauchy problem for a Boussinesq type equation of sixth order with the nonlinear term f(u)f(u) behaving as up(p>1) as u→0u→0 in Rn,n≥1. The main method and techniques used in our paper are the Littlewood–Paley dyadic decomposition, the stationary phase estimate and some properties of Bessel function.