A stochastic Benjamin-Bona-Mahony type equation

TL;DR

This paper studies a stochastic nonlinear dispersive equation modeling surface water waves with uncertainty, focusing on the initial-value problem and ensuring energy conservation through a Hamiltonian framework.

Contribution

It introduces a Hamiltonian-based stochastic model for water waves and analyzes the well-posedness of its initial-value problem.

Findings

Energy conservation is maintained in the stochastic model.

The initial-value problem is well-posed under the proposed formulation.

Abstract

Considered herein is a particular nonlinear dispersive stochastic equation. It was introduced recently in [3], as a model describing surface water waves under location uncertainty. The corresponding noise term is introduced through a Hamiltonian formulation, which guarantees the energy conservation of the flow. Here the initial-value problem is studied.