Well-posedness of a highly nonlinear shallow water equation on the circle
Analysis of PDEs
2020-11-04 v1
Abstract
We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space on the circle for .
Cite
@article{arxiv.2011.01290,
title = {Well-posedness of a highly nonlinear shallow water equation on the circle},
author = {Nilay Duruk Mutlubas and Anna Geyer and Ronald Quirchmayr},
journal= {arXiv preprint arXiv:2011.01290},
year = {2020}
}