Well-posedness and scattering of small amplitude solutions to Boussinesq paradigm equation

Abstract

This paper studies the existence and scattering of global small amplitude solutions to the nonlinear Boussinesq paradigm equation in Rn. Firstly, with a dispersive estimate obtained by oscillatory integral and some properties of Bessel function, the existence of global small amplitude solutions is established by the method of contractive mapping principle. Then, with the help of the decay of solutions with respect to time, we construct the suitable scattering state corresponding to the small amplitude solutions.