Global-in-time existence of perturbations around travelling-waves

TL;DR

This paper proves the global-in-time well-posedness of solutions near travelling-waves for a fractional diffusion/anti-diffusion equation modeling sand dune dynamics under fluid flow.

Contribution

It establishes the first rigorous proof of global existence of solutions around travelling-waves for Fowler's fractional equation.

Findings

Global-in-time existence near travelling-waves

Well-posedness of the Fowler equation

Rigorous mathematical validation of dune dynamics model

Abstract

We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-in-time well-posedness in the neighbourhood of travelling-waves solutions of the Fowler equation.