Existence and scattering theory for Boussinesq type equations with singular data

We study the initial value problem for the generalized Boussinesq equation and prove existence of local and global solutions with singular initial data in weak-Lp spaces. Our class of initial data for global existence is larger than that of Cho and Ozawa (2007) [7]. Long time behavior results are obtained and a scattering theory is proved in that framework. With more structure, we show Sobolev H1 and Lorentz-type L(p,q) regularity properties for the obtained solutions. The approach employed is unified for all dimensions n⩾1.