Whitham's equations for modulated roll-waves in shallow flows
Analysis of PDEs
2010-11-11 v1
Abstract
This paper is concerned with the detailed behaviour of roll-waves undergoing a low-frequency perturbation. We rst derive the so-called Whitham's averaged modulation equations and relate the well-posedness of this set of equations to the spectral stability problem in the small Floquet-number limit. We then fully validate such a system and in particular, we are able to construct solutions to the shallow water equations in the neighbourhood of modulated roll-waves proles that exist for asymptotically large time.
Cite
@article{arxiv.1011.2296,
title = {Whitham's equations for modulated roll-waves in shallow flows},
author = {Pascal Noble and Luis Miguel Rodrigues},
journal= {arXiv preprint arXiv:1011.2296},
year = {2010}
}