On the well-posedness of a weakly dispersive Boussinesq system

Abstract

We study the Cauchy problem for one-dimensional dispersive system of Boussinesq type which models weakly nonlinear long wave surface waves. We establish the local well-posedness and ill-posedness of solutions to the system. We also provide criteria for the formation of singularities.

20 pages

References in corpus (1)

• On the regularity of the flow map for the gravity-capillary equations