A KdV-type Boussinesq system: From the energy level to analytic spaces

Abstract

Considered here is the well-posedness of a KdV-type Boussinesq system modeling two-way propagation of small-amplitude long waves on the surface of an ideal fluid when the motion is sensibly two dimensional. Solutions are obtained in a range of Sobolev-type spaces, from the energy level to the analytic Gevrey spaces. In addition, a criterion for detecting the possibility of blow-up in finite time in terms of loss of analyticity is derived.