A conditional well-posedness result for the bidirectional Whitham equation
Analysis of PDEs
2017-08-16 v1
Abstract
We consider the initial-value problem for the bidirectional Whitham equation, a system which combines the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow-water nonlinearity. We prove local well-posedness in classical Sobolev spaces in the localised as well as the periodic case, using a square-root type transformation to symmetrise the system. The existence theory requires a non-vanishing surface elevation, indicating that the problem is ill-posed for more general initial data.
Keywords
Cite
@article{arxiv.1708.04551,
title = {A conditional well-posedness result for the bidirectional Whitham equation},
author = {Mats Ehrnström and Long Pei and Yuexun Wang},
journal= {arXiv preprint arXiv:1708.04551},
year = {2017}
}