Cauchy problem for a higher-order boussinesq equation /

Abstract

In this thesis, we establish global well-posedness of the Cauchy problem for a particular higher-order Boussinesq equation. At the microscopic level this sixth order Boussinesq equation was derived in [11] for the longitudinal vibrations of a dense lattice, in which a unit length of the lattice contains a large number of lattice points. We take the initial data in the Sobolev space Hs with s > 1 2 . With smoothness assumptions on the nonlinear term, we establish local existence and uniqueness of the solution. Under further assumptions, we prove the global existence for s 1. Finally, we show continuous dependence of the solution on the initial data.