Well-posedness for a dispersive system of the Whitham-Boussinesq type
Analysis of PDEs
2019-12-17 v3
Abstract
We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive dispersive and Strichartz estimates, and implement them together with a fixed point argument to solve the problem locally. Hamiltonian conservation guarantees global well-posedness for small initial data in the one dimensional settings.
Keywords
Cite
@article{arxiv.1902.09438,
title = {Well-posedness for a dispersive system of the Whitham-Boussinesq type},
author = {Evgueni Dinvay and Sigmund Selberg and Achenef Tesfahun},
journal= {arXiv preprint arXiv:1902.09438},
year = {2019}
}