Wellposedness and scattering for the generalized Boussinesq equation

Abstract

In this paper, we show the local well-posedness of the generalized Boussinesq equation(gBQ) in $L^2({\mathbb{R}}^d),H^1({\mathbb{R}}^d)$ and obtain the global well-posedness, finite-time blowup and small initial data scattering of gBQ in energy space $H^1({\mathbb{R}}^d)$. Moreover, we obtain the large radial initial data scattering of defocusing case for $d\ge 3$ by using the method of Dodson-Murphy.

References in corpus (1)

• A sharp condition for scattering of the radial 3d cubic nonlinear Schroedinger equation