Existence and Uniqueness for a Boussinesq System with a Disordered Forcing

Abstract

We study the existence, uniqueness, regularity and continuous dependence on initial data of solutions for the Cauchy problem associated with the coupled system of Boussinesq type equations forced by highly oscillatory smooth coefficients. The model considered describes two-way propagation of long water waves with small amplitude on the surface of a one-dimensional channel with rough bottom (disordered topography). The dependent variables in this model are the wave n elevation and the potential velocity u measured at the fixed depth Z₀ = square root of 2/3.