Existence and asymptotic decay for a Boussinesq-type model

In this article, we study the initial value problem associated with a five-parameter Boussinesq-type system. We prove local existence and uniqueness of the solution and that the supremum norm of the solution decays algebraically to zero as (1+t)−1/3 when t approaches to infinity, provided the initial data are sufficiently small and regular. We further present a high-accurate spectral numerical method to approximate the solutions and validate the theoretical results.